Transcript Solving Application Problems

MTH 10905
Algebra
SOLVING APPLICATION
PROBLEMS
CHAPTER 3 SECTION 2
Use the Problem Solving Procedure
 To solve application problems you must answer the question asked.
 We often translate into mathematically terms without realizing it.
 For example: You need three cups of milk for a recipe. Your measuring
cup holds 2 cups. You reason that you will need one additional cup.
Let x = additional cups needed
2 cups + additional = total
2+x=3
Solve
x=3–2
x=1
we will need one additional cup.
Use the Problem Solving Procedure
 Five-step problem solving procedure:
1.
Understand the Problem – Identify the quantity or quantities you are being
asked to find.
2.
Translate the problem into mathematical language (express the problem as an
equation).
1.
Choose a variable to represent one quantity, write down exactly what it
represents.
2.
Using this information write the equation that represents the application.
3.
Carry out the mathematical calculations (solve the equation).
4.
Check the answer (using the original application).
5.
Answer the question asked.
Setup and Solve Number Application Problems
Exp:
Four subtracted from three times a
number is 11. Find the number.
1. What are we asked to do?
1. Find an unknown number
2. Translate the problem.
2. Let x = the unknown number.
3. Write the equation.
3.
3x – 4 = 11
4.
3x – 4 = 11
3x – 4 + 4 = 11 + 4
3x = 15
x = 15/3 = 5
4. Solve:
5. Check:
3x – 4 = 11
3(5) – 4 = 11
15 – 4 = 11
11 = 11
The number is 5
Setup and Solve Number Application Problems
Exp:
The difference of two numbers is 16. Find the two numbers if the
larger number is 2 less than the 4 times the smaller.
Let x = smaller number
4x – 2 = larger number
(4x – 2) – x = 16
4x – 2 – x = 16
3x – 2 = 16
3x = 18
x = 18/2 = 6
x = 6 smaller number
Check:
4x – 2 – x = 16
(4)(6) – 2 – 6 = 16
24 – 2 – 6 = 16
22 – 6 = 16
22 = 22
4x – 2= (4)(6) – 2 = 22 larger number
Setup and Solve Number Application Problems
Exp:
Carol is older than Liz. Carol is four years older than 3 times Liz’s
age. The difference between Carol’s and Liz’s age is 10 years.
Determine Liz’s age.
Let x = Liz’s age
3x + 4 = Carol’s age
(3x + 4) – x = 10
3x + 4 – x = 10
2x + 4 = 10
2x = 6
x = 6/2 = 3
Liz is 3 years old
and
Carol is 3(3) + 4 = 9 + 4 = 13 years old
Setup and Solve Number Application Problems
Exp:
A company presently has a cash reserve of $30,000. It plans to add
$2,500 a month to the reserve until the reserve reaches $55,000.
How long will it take the company to reach its goal?
Let x = # of months
2,500x = amount for x months
30,000 + 2,500x = 55,000
2,500x = 55,000 – 30,000
2,500x = 25,000
x = 25,000/2,500 = 10
It will take the company 10 months to reach its goal.
Setup and Solve Application Problems involving Money
Exp:
A truck rental cost $42 a day plus 24 cents a mile. If the total cost
for 1 day rental is $63.60 how many miles were driven?
Let x = number of miles
0.24x = cost for x miles
42 + 0.24x = 63.60
0.24x = 63.60 – 42
0.24x = 21.60
x = 21.60/0.24 = 90
The mileage driven was 90.
Setup and Solve Application Problems involving Money
Exp:
The cost of having a load of rubbish picked up by Waste
Management is $49 plus 30 cents per pound of rubbish. The cost of
having rubbish picked up by Sun City Disposal is $89 plus 10 cents
per pound of rubbish. How many pounds of rubbish would need to
be picked up to make the cost of both pickups the same?
49 + 0.30x = Waste Management – Less than 200 lbs pick this one
89 + 0.10x = Sun City Disposal – More than 200 lbs pick this one
49 + 0.30x = 89 + 0.10x
0.30x – 0.10x = 89 – 49
0.20x = 40
x = 200
You would need to have 200 lbs of rubbish removed to have equal cost.
Setup and Solve Applications Concerning Percents
Exp:
The cost a meal and a 7% tax is $16.26. Find the cost of the meal
before tax.
x = cost of meal before tax
0.07x = tax on meal
x + 0.07x = 16.26
1.07x = 16.26
x = 15.20
The cost of the meal before tax was $15.20.
Setup and Solve Applications Concerning Percents
Exp:
The number of people who signed up for the company picnic this
year is 10% greater than the number who signed up for the last year’s
picnic. If 253 people signed up for this year’s picnic, find the
number of people who signed up for last years picnic.
x = number who signed up last year
0.10x = amount of increase
x + 0.10x = 253
1.10x = 253
x = 230
The number of people who signed up for last years picnic was 230.
Setup and Solve Applications Concerning Percents
Exp:
The salary plan is $30,000 a year plus 6% commission of sales. A
second plan is $40,000 a year plus 4% commission of sales. At what
sales will the two plans give the same salary.
Let x = amount of sales
30,000 + 0.06x = first plan – Take this job if more than $500,000
40,000 + 0.04x = second plan – Take this job if less than $500,000
30,000 + 0.06x = 40,000 + 0.04x
0.06x – 0.04x = 40,000 – 30,000
0.02x = 10,000
x = 500,000
You need to sale $500,000 in order for the plans to be equal.
HOMEWORK 3.2
 Page 201 - 202
#5, 7, 11, 13, 15