Transcript Chapter 6 - Crestwood Local Schools

Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
Write three fractions equivalent to 4 .
12
Sample answers
1
3
,
2, 6
6 18
6-1
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
(For help, go to Lesson 4-4.)
Write in simplest form.
1. 30
2. 24
3. 54
4. 12
5. 14
6. 40
35
15
40
60
42
24
Check Skills You’ll Need
6-1
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
Solutions
30
30 ÷ 5
1. 35 = 35 ÷ 5
24
6
= 7
54
54 ÷ 6
3. 60 = 60 ÷ 6
3
= 5
12
9
14
14 ÷ 14
12 ÷ 3
4. 15 = 15 ÷ 3
4
= 10
5. 42 = 42 ÷ 14
24 ÷ 8
2. 40 = 40 ÷ 8
= 5
40
40 ÷ 8
6. 24 = 24 ÷ 8
1
5
= 3 =12
3
= 3
6-1
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
A survey asked students whether they had afterschool jobs. Write each ratio as a fraction in simplest form.
a. all students surveyed to students
without jobs
all students surveyed
students without jobs
= 100
Response
60
5
=
3
b. all students surveyed to students
with jobs
all students surveyed
students with jobs
After-School Jobs
Number
Have a Job
40
Don’t Have a Job
60
Total
100
= 100
40
5
=
2
Quick Check
6-1
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
The table shows prices for different packages of index
cards. Which size has the lowest unit price?
Size
(cards) Price
100
$2.70
50
$1.30
25
$.75
100 cards:
price
number of cards
$2.70
100 cards
= $.027/card
50 cards:
price
number of cards
$1.30
50 cards
Find the
= $.026/card unit prices.
25 cards:
price
number of cards
$0.75
25 cards
= $.03/card
The 50-card pack has the lowest unit price.
6-1
Quick Check
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
Convert 30 gal/min to cups/second.
30 gal
16 c
30 gal/min = 1 min • 1 gal
130
gal
= 1 min
816
c
• 1 gal
1 min
• 60 s
•
1 min
260 s
Use conversion factors that convert
gallons to cups and minutes to
seconds.
Divide the common factors
and units.
1
8c
Simplify.
= s
30 gal/min equals 8 c/s.
Quick Check
6-1
Ratios and Unit Rates
PRE-ALGEBRA LESSON 6-1
Write each ratio as a fraction in simplest form.
1. 4 out of 20 students ride the bus to school.
1
5
2. 8 out of 10 students buy lunch.
4
5
Find each unit rate.
3. You pay $4.50 for 2 gallons of orange juice.
$2.25/gal
4. You pay $21.60 for a 20-lb bag of dog food.
$1.08/lb
5. Convert 15 yd/min to inches/second.
9 in./s
6-1
Proportions
PRE-ALGEBRA LESSON 6-2
Evaluate each of the following operations for n = 6.
a. Multiply n by 4 and add 6.
30
b. Multiply n by 9 and add 12
66
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
(For help, go to Lesson 2-6.)
Solve each equation.
1. 4x = 52
2. 3y = 18
3. 5b = 75
4. 7k = 21
Check Skills You’ll Need
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
Solutions
1. 4x = 52
4x
4
=
2. 3y = 18
52
4
3y
3
x = 13
3. 5b = 75
5b
5
=
=
18
3
y=6
4. 7k = 21
75
5
7k
7
b = 15
=
21
7
k=3
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
Solve
Method 1
2
y
=
.
7
14
Multiplication Property of Equality
2
y
=
7
14
2
• 14 = y • 14
7
14
28 = y
7
4 =y
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
(continued)
Method 2
Cross products
2
y
=
7
14
2 • 14 = 7 • y
28 = 7y
28 7y
=
7
7
4 =y
Quick Check
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
Do the ratios 3 and 21 form a proportion? Explain.
5
3
5
3 • 35
35
21
35
Test by writing as a proportion.
5 • 21
Write cross products.
105 = 105
Simplify.
Yes; the ratios do form a proportion. The cross products
are equal.
Quick Check
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
One hundred rods is about 275 fathoms. About how many
fathoms is 25 rods?
Let d = distance in fathoms.
length in rods
length in fathoms
100d = 275(25)
d=
275(25)
100
d = 68.75
100
25
=
275
d
distance in rods
distance in fathoms
Write cross products.
Divide each side by 100.
Simplify.
25 rods is about 68.75 fathoms.
Quick Check
6-2
Proportions
PRE-ALGEBRA LESSON 6-2
Solve each proportion.
1. a = 5
12 6
10
2. 3 = 6
8
x
16
Does each pair of ratios form a proportion? Explain.
2
0.4
3. 9 = 1.8
Yes; the cross
products are equal.
21
14
4. 50 = 25
No; the cross products
are not equal.
5. 100 nautical miles equals about 115 statute miles. About how far in `
nautical miles is 50 statute miles? Round to the nearest whole
number.
about 43 nautical miles
6-2
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
Find each value of n.
a. 18 = n
15
5
n=6
b. 1.5
n
= 2.7
4.5
n = 0.9
6-3
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
(For help, go to Lesson 6-2.)
Solve each proportion. Round to the nearest tenth where necessary.
2
f
9
15
1. 3 = 21
3. 4 = p
3
50
16
19
2. 8 = p
4. 3 = g
Check Skills You’ll Need
6-3
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
Solutions
1.
2
f
=
3
21
2.
3
50
=
8
p
3.
9
15
=
4
p
4.
16 19
= g
3
3 • f = 2 • 21
8 • 50 = 3 • p
4 • 15 = 9 • p
3 • 19 = 16 • g
3f = 42
400 = 3p
60 = 9p
57 = 16g
3f
42
=
3
3
400
3p
=
3
3
60
9p
=
9
9
57
16g
=
16
16
6.7 = p
3.6 = g
f = 14
133.3 = p
6-3
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
Trapezoid ABCD ~ trapezoid EFGH. Find the
value of k.
Write a proportion for corresponding sides.
Side AB corresponds
to side EF.
6
= 3
k
2
Side CD corresponds
to side GH.
6 • 2 = k • 3 Write cross products.
6•2
3k
=
3
3
4=k
Divide each side by 3.
Simplify.
6-3
Quick Check
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
A flagpole casts a shadow 5 ft long. At the same time, a
yardstick casts a shadow 1.5 ft long. The triangle shown for the flagpole
and its shadow is similar to the triangle shown for the yardstick and its
shadow. How tall is the flagpole?
1.5 3
=
5
x
Corresponding sides of similar
triangles are in proportion.
1.5x = 5 • 3
Write cross products.
1.5x 5 • 3
=
1.5
1.5
Divide each side by 1.5.
x = 10
Simplify.
The flagpole is 10 ft tall.
Quick Check
6-3
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
The scale of a map is 1 in. : 24 mi. About how far is it between
two cities that are 3 in. apart on the map?
map (in.)
actual (mi.)
1
3
=
24 d
map (in.)
actual (mi.)
1 • d = 24 • 3
d = 72
Write a proportion.
Write cross products.
Simplify.
It is about 72 mi between the two cities.
Quick Check
6-3
Similar Figures and Scale Drawings
PRE-ALGEBRA LESSON 6-3
Solve.
1. Parallelogram ABCD ~ parallelogram EFGH.
Find the value of x.
12
2. A girl who is 4 feet tall casts a shadow that is 6 feet
long. The tree next to her casts a shadow that is 12
feet long. How tall is the tree?
8 ft
3. The scale on a map is 3 in. : 100 mi. What is the actual
distance between two towns that are 9 in. apart on the
map?
300 mi
6-3
Probability
PRE-ALGEBRA LESSON 6-4
Forty-three boys and five girls tried out for the middle school football
team. One-fourth of the students were dropped after the first day. Of
those who were left, 1 were dropped after the second day. Of those
6
4
who remained, made the team. How many students made
5
the team?
24
6-4
Probability
PRE-ALGEBRA LESSON 6-4
(For help, go to Lesson 5-3.)
Simplify.
3. 1 –
17
3
2. 1 – 20
6
11
4. 1 – 12
1. 1 – 8
1
Check Skills You’ll Need
6-4
Probability
PRE-ALGEBRA LESSON 6-4
Solutions
1. 1 – 3
2. 1 – 17
8
8
3
8–3
– =
8
8
8
5
= 8
3.
20
20 17
20 – 17
–
=
20 20
20
3
= 20
6
11
11
6
11 – 6
–
=
11
11
11
5
=
11
4. 1 – 1
1–
12
12
1
12 –1
–
=
12
12
12
11
=
12
6-4
Probability
PRE-ALGEBRA LESSON 6-4
Find P(rolling a prime number) with one number cube.
3
number of favorable outcomes
= 6
number of possible outcomes
3
3 prime-number outcomes (2, 3, 5)
6 possible outcomes
1
P(rolling a prime number) = 6 , or 2 .
Quick Check
6-4
Probability
PRE-ALGEBRA LESSON 6-4
The probability that a child is an identical twin is 4 in 1,000.
Find P(not an identical twin).
P(not an identical twin) + P(identical twin) = 1
Write an equation.
4
P(not an identical twin) + 1,000 = 1
P(not an identical twin) +
Substitute.
4
– 4
=1 – 4
1,000
1,000
1,000
996
P(not an identical twin) = 1,000
=
Subtract
4
from
1,000
each side.
Simplify.
249
250
The probability that a child is not an identical twin is 249 .
250
6-4
Quick Check
Probability
PRE-ALGEBRA LESSON 6-4
You have five different coins in your pocket: a penny, a
nickel, a dime, a quarter, and a half-dollar. You pull out one coin at
random. What are the odds in favor of the coin being worth less
than ten cents?
2
odds in favor = 3
The odds are
2 are worth less than ten cents.
3 are not.
2
, or 2 to 3, in favor of the coin being worth less than ten cents.
3
Quick Check
6-4
Probability
PRE-ALGEBRA LESSON 6-4
Find each probability.
1. A letter is selected at random from the letters A, E, I,
O, and U. Find the probability that the letter is an A.
1
5
2. In one class, Ms. Lang has 8 boys and 12 girls. She
needs to choose one student to help pass out papers.
What are the odds that a girl is chosen?
3
2
3. When rolling a number cube, what is P(6)? What is
P(not 6)?
1; 5
6 6
6-4
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
5
Samantha needs a 8 -in. bit for her drill. Should she look in the bin
marked 62.5 in., 6.25 in., 0.625 in., or 0.063 in.?
0.625 in.
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
(For help, go to Lesson 5-2.)
Write each fraction as a decimal.
5
1. 8
4.
5
6
9
2. 20
5.
2
3
3.
3
4
8
6. 11
Check Skills You’ll Need
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Solutions
1.
5
=5÷8
8
2.
9
= 9 ÷ 20
20
= 0.625
= 0.45
4. 6 = 5 ÷ 6
= 0.83
5. 3 = 2 ÷ 3
= 0.6
5
2
6-5
3.
3
=3÷4
4
= 0.75
8
6. 11 = 8 ÷ 11
= 0.72
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Write each percent as a fraction or a mixed number.
a. 30%
30
100
Write as a fraction with a denominator of 100.
3
10
Simplify.
b. 175%
175
100
Write as a fraction with a denominator of 100.
7
4
Simplify.
13
4
Write as a mixed number.
Quick Check
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Express 7.3% as a decimal.
7.3% =
7.3
100
= 007.3
Write as a fraction with a denominator of 100.
Divide by moving the decimal point two places to
the left. You may need to write one or more zeros.
= 0.073
Quick Check
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Express 0.412 as a percent.
Method 1
0.412 =
Rewrite as a fraction.
412
1,000
=
412 ÷ 10
1,000 ÷ 10
=
41.2
100
= 41.2%
Method 2
Move the decimal point.
0.412 = 41.2%
Quick Check
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Four out of seven members of the chess club are boys.
What percent of the chess club members are boys?
4
7
Write a fraction.
0.5714
Divide the numerator by the denominator.
57.14%
Write as a percent.
About 57% of the chess club members are boys.
Quick Check
6-5
Fractions, Decimals, and Percents
PRE-ALGEBRA LESSON 6-5
Write each percent as a fraction or mixed number, and as a decimal.
1. 325%
13 , or 3 1 ; 3.25
4
4
2. 1.1%
11 ; or 0.011
1,000
Write each as a percent.
3. 2.01
201%
3
4. 5
60%
5. Six out of fifteen students own skateboards. What percent of
students own skateboards?
40%
6-5
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
A painter uses 3 cans of paint to paint four sets of shelves. How many
cans of paint does he need to buy to paint nine sets of shelves?
7 cans
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
(For help, go to Lesson 6-2.)
Solve each proportion.
25
x
1. 100 = 28
2.
98.9
43
=
x
100
13
52
= x
100
4.
27
x
= 150
100
3.
Check Skills You’ll Need
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
Solutions
1.
25
x
=
100 28
2.
100 • x = 25 • 28
100x = 700
43 • x = 98.9 • 100
43x = 9890
100x 700
100 = 100
43x 9890
43 = 43
x =7
3.
98.9
43
=
x
100
x = 230
52
13
=
100
x
4.
x
27
=
100
150
13 • 100 = 52 • x
1300 = 52x
100 • 27 = x • 150
2700 = 150x
1300 = 52x
52
52
2700 = 150x
150
150
25 = x
18 = x
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
Find 23% of 158.
23
n
=
100
158
Write a proportion.
23(158) = 100n
Write cross products.
23(158)
100n
=
100
100
Divide each side by 100.
36.34 = n
Simplify.
23% of 158 is 36.34.
Quick Check
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
What percent of 34 is 28? Round to the nearest tenth
of a percent.
n
28
=
100
34
Write a proportion.
34n = 100(28)
Write cross products.
100(28)
34n
=
34
34
Divide each side by 34.
n = 82.35...
Simplify.
82.4
Round.
28 is approximately 82.4% of 34.
6-6
Quick Check
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
216 is 72% of what number?
72
216
=
100
n
Write a proportion.
72n = 100(216)
Write cross products.
72n 100(216)
=
72
72
Divide each side by 72.
n = 300
Simplify.
216 is 72% of 300.
Quick Check
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
A tile floor has 90 blue tiles, which is 15% of all the tiles in
the floor. How many tiles are in the floor in all?
90
15
= x
100
Write a proportion.
15x = 100(90)
Write cross products.
100(90)
15x
=
15
15
Divide each side by 15.
x = 600
Simplify.
The floor has 600 tiles in all.
Check. Is the answer reasonable? The problem says the number of
blue tiles is 15%. 10% of 600 is 60, so 5% of 600 is 30, and
15% is 60 + 30 = 90. The answer is reasonable.
Quick Check
6-6
Proportions and Percents
PRE-ALGEBRA LESSON 6-6
Solve.
1. Find 47% of 2,400.
2. What percent of 700 is 1,498?
1,128
214%
3. 6 is 3% of what number?
200
4. Water covers about 361,736,000 km2, or about 70.8% of Earth’s
surface. What is the approximate surface area of Earth?
about 511,000,000 km2
6-6
Percents and Equations
PRE-ALGEBRA LESSON 6-7
Match each expression in Column 1 with an equivalent
expression in Column 2.
Column 1
1. 50% of 250
2. 100% of 250
3. 1% of 250
4. 10% of 250
Column 2
a. 250
b. 2.5
c. 25
d. 125
1. d 2. a 3. b 4. c
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
(For help, go to Lesson 6-5.)
Write each percent as a decimal.
1. 48%
2. 5%
3. 23.8%
4. 72.25%
5. 136%
6. 178.5%
Check Skills You’ll Need
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
Solutions
48
1.
48% = 100
= 0.48
3.
23.8% =
2.
23.8
100
4. 72.25% =
= 0.238
5. 136% =
5
5% = 100
= 0.05
72.25
100
= 0.7225
136
100
6. 178.5% =
= 1.36
178.5
100
= 1.785
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
What is 35% of 84?
n = 0.35 • 84
Write an equation. Write the percent as a decimal.
n = 29.4
Simplify.
35% of 84 is 29.4.
Quick Check
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
What percent of 26 is 65?
n • 26 = 65
26n
65
=
26
26
n = 2.5
= 250%
Write an equation.
Divide each side by 26.
Simplify.
Change the decimal to a percent.
65 is 250% of 26.
Quick Check
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
A car salesman makes a 6.5% commission on each car he
sells. How much does he make on the sale of a car for $35,000?
Words
amount of
commission
is
6.5%
of
$35,000
•
$35,000
Let c = amount of commission.
Equation
c
=
0.065
c = 0.065 • 35,000
= 2,275
The salesman’s commission is $2,275.
6-7
Quick Check
Percents and Equations
PRE-ALGEBRA LESSON 6-7
During a telephone survey, 414 people, or 46% of those
called, said that they were watching station RFGT at the time of the
call. How many people were called?
Words
Equation
414
is
46%
of
people called
Let n
= number of people called.
414
=
0.46
•
n
0.46n = 414
0.46n
414
=
0.46
0.46
n = 900
Quick Check
900 people were called.
6-7
Percents and Equations
PRE-ALGEBRA LESSON 6-7
Solve
1. What is 9% of 30?
2. What is 25% of 312?
2.7
78
3. What percent of 9 is 3?
4. What percent of 3 is 9?
1
300%
33 3 %
5. A car dealer makes an 8% commission on each car she sells. How
much does she make on a $40,000 sale?
$3,200
6. During a telephone survey, 320 people, or 25% of those called, said
they were listening to the same station at the time of the call. How
many people were called?
1,280 people
6-7
Percent of Change
PRE-ALGEBRA LESSON 6-8
Write these fractions to the nearest tenth of a percent.
a. 65
255
25.5%
b. 42
52
80.8%
6-8
Percent of Change
PRE-ALGEBRA LESSON 6-8
(For help, go to Lesson 6-5.)
Write each decimal as a percent.
1. 0.46
2. 2.47
3. 0.03
4. 5.236
Check Skills You’ll Need
6-8
Percent of Change
PRE-ALGEBRA LESSON 6-8
Solutions
1. Move the decimal 2 places to the right. 0.46 = 46%
2. 2.47 = 247%
3. 0.03 = 3%
4. 5.236 = 523.6%
6-8
Percent of Change
PRE-ALGEBRA LESSON 6-8
Find the percent of increase from 8 to 9.6.
amount of increase = 9.6 – 8 = 1.6
percent of increase =
amount of increase
original amount
1.6
= 8
= 0.2 = 20%
The percent of increase from 8 to 9.6 is 20%.
Quick Check
6-8
Percent of Change
PRE-ALGEBRA LESSON 6-8
In a given year, Hillsboro had a total of 7.5 in. of rain by
March 1 and a total of 22.5 in. by July 1. Find the percent of
increase from 7.5 to 22.5.
amount of increase = 22.5 – 7.5 = 15
percent of increase =
amount of increase
original amount
15
= 7.5
= 2 = 200%
The percent of increase from March 1 to July 1 was 200%.
6-8
Quick Check
Percent of Change
PRE-ALGEBRA LESSON 6-8
Find the percent of decrease from 1,250 to 1,120.
amount of decrease = 1,250 – 1,120 = 130
percent of decrease =
=
amount of decrease
original amount
130
1,250
= 0.104 = 10.4%
Quick Check
6-8
Percent of Change
PRE-ALGEBRA LESSON 6-8
Solve.
1. Find the percent of increase from 22 to 63.
186.4%
2. Find the percent of decrease from 6.3 to 2.2.
65.1%
3. A surgeon performed 62 operations in 1991. He performed
342 in 2001. Find the percent of increase.
451.6%
6-8
Markup and Discount
PRE-ALGEBRA LESSON 6-9
Without computing, explain why 40% of 22 is less than 11.
11 is half, or 50%, of 22, so 40% of 22 is less than 11.
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
(For help, go to Lesson 6-7.)
Write an equation and solve. Round to hundredths as needed.
1. What is 75% of $82?
2. What is 42% of $170?
3. What is 5.5% of $24?
4. What is 80% of $15.99?
Check Skills You’ll Need
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
Solutions
1. What is 75% of $82?
n = 0.75 • 82
n = 61.5
75% of $82 is $61.50.
2. What is 42% of $170?
n = 0.42 • 170
n = 71.4
42% of $170 is $71.40.
3. What is 5.5% of $24?
n = 0.055 • 24
n = 1.32
5.5% of $24 is $1.32.
4. What is 80% of $15.99?
n = 0.80 • 15.99
n = 12.79
80% of $15.99 is $12.79.
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
A grocery store has a 20% markup on a can of soup.
The can of soup costs the store $1.25. Find the markup.
markup = percent of markup • store’s cost
= 0.2 • 1.25
= 0.25
Simplify.
The markup is $.25.
Quick Check
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
A bookstore pays $4.50 for a novel. The percent of
markup is 45%. Find the novel’s selling price.
0.45 • 4.50 = 2.03
Multiply to find the markup.
4.50 + 2.03 = 6.53
Store’s cost + markup = selling price.
The selling price is $6.53.
Quick Check
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
A camera that regularly sells for $210 is on sale for 30%
off. Find the discount.
discount = percent of discount • regular price
= 0.30 • 210
= 63
The discount is $63.
Quick Check
6-9
Markup and Discount
PRE-ALGEBRA LESSON 6-9
Solve.
1. The school store has a 65% markup on each stapler. Each stapler
costs the store $2.10. Find the markup.
$1.37
2. A clothes store pays $40 for a skirt. The percent of markup is 25%.
Find the skirt’s selling price.
$50
3. A pair of shoes that regularly sells for $94.99 is on sale for 30% off.
What is the sale price?
$66.49
6-9
Problem Solving Strategy: Make a Table
PRE-ALGEBRA LESSON 6-10
A theater has 25 seats in the first row. Each of the following rows
has two more seats than the row before it. How many seats are in
the 15-row theater?
585
6-10
Problem Solving Strategy: Make a Table
PRE-ALGEBRA LESSON 6-10
(For help, go to Lesson 1-8.)
Solve.
1. For two weeks, you double the amount of money you save each day.
You save $.01 the first day. How much money will you have at the
end of the two weeks?
Check Skills You’ll Need
6-10
Problem Solving Strategy: Make a Table
PRE-ALGEBRA LESSON 6-10
Solutions
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Amount of new money saved
$.01
$.02
$.04
$.08
$.16
$.32
$.64
$1.28
$2.56
$5.12
$10.24
$20.48
$40.96
$81.92
Total amount saved
$.01
1 + 2 = $.03
3 + 4 = $.07
7 + 8 = $.15
15 + 16 = $.31
31 + 32 = $.63
63 + 64 = $1.27
1.27 + 1.28 = $2.55
2.55 + 2.56 = $5.11
5.11 + 5.12 = $10.23
10.23 + 10.24 = $20.47
20.47 + 20.48 = $40.95
40.95 + 40.96 = $81.91
81.91 + 81.92 = $163.83
After 2 weeks, $163.83 will have been saved.
6-10
Problem Solving Strategy: Make a Table
PRE-ALGEBRA LESSON 6-10
Martin had 100 trees in his orchard the first year. Each
year after that he increased the number of trees in his orchard by
10%, rounded to the nearest whole number. How many trees did he
have in his orchard in the sixth year?
Year
1
2
3
4
5
6
Tree Count at
Beginning of
Year
100
110
121
133
146
161
Rate of
Increase
(10%)
0.1
0.1
0.1
0.1
0.1
Martin had 161 trees in the sixth year.
6-10
Increase in
Tree Count
Tree Count at
End of Year
10
11
12
13
15
110
121
133
146
161
Quick Check
Problem Solving Strategy: Make a Table
PRE-ALGEBRA LESSON 6-10
Solve.
1. For an auction item, the bid starts at $100 and increases 50%
every minute. In how many minutes will the bid go over $2,500?
8 minutes
2. Sharon uses her initials, SLF, for her password. How many
different three-letter passwords can she make with these letters?
6 passwords
3. In how many ways can you make 45¢ in change using only nickels,
dimes, and quarters?
8 ways
6-10