Transcript Equations-Modeling Real World Problems

Do Now
Use the information in the table to determine whether the rule works for the
given input-output pair. Write “Yes” if the rule works for the input-output pair
and “No” if it does not. Write the rule that works for all pairs.
Modeling Using Equations
Let’s practice looking for a pattern and describing it in words.
Believe it or not, there is a relationship between input and output
in the tables below. Write an input-output rule in words to
describe each relationship.
Input
Output
Input
Output
apple
e
sing
16
egg
g
chair
25
hour
r
is
4
and
d
a
1
eight
t
revolve
49
Let’s look for more rules!!!
Find a rule for each input-output table. State your rule in
two different ways: (1) as a sentence; and (2) as an equation.
x
Process
y
x
Process
y
-0.5
7.5
0
7
0
8
3
4
0.5
8.5
5
2
1
9
-5
12
1.5
9.5
-1
8
Link to the Real World
Mia is ordering CDs from an online store. Each CD
costs $5, and the shipping fee is $10, no matter how many
CDs she orders. For example, if she orders 3 CDs, then the payment
will be $25. Find four more possibilities for the number of CDs
ordered. Fill in the table below. Then write a rule relating the
number of CDs ordered, C, to the payment amount, P.
C
3
Process
P
Rule:
25
How can you use your rule to
determine how much it will
cost if Mia orders 25 CDs?
Now You Try!!
Romero and his brother Nelson love to play video games. Right
now, Romero’s score is 11 less than 2 times Nelson’s score. For
example, if Nelson has 80 points, than Romero has 149 points. Find
four more possibilities for the brothers’ scores and fill in the table
below. Then write a rule relating Romero’s score, R, to Nelson’s
score, N.
N
80
Process
R
Rule:
149
How many points will Romero have
if Nelson has 5072 points?
Explain how you used your rule to
find Romero’s score.
Now You Try!!
Wes mows lawns in the summer. He charges the same fixed amount
for each lawn that he mows. As of today, he has earned $36 after
mowing 3 lawns.
a. Create an input-output table using the headings “Number of lawns mowed”
for the input and “Amount of money in dollars” for the output. Fill in the
appropriate values for Wes’ situation. Then fill in several other rows of
information that fit the situation. For example, what if he mows 8 lawns?
b. Use any patterns you see in your input-output table to find a rule relating
the number of lawns mowed and the amount of money in dollars.
c. Explain how you know that your rule works.
d. Wes wants to go to a 2-day music festival. Tickets for the festival cost $190.
How many lawns will Wes need to mow this summer to earn enough money
to buy a ticket? Show how you got your answer.
More Modeling Using Equations
Before looking at more situations where we can use
equations to find solutions, let’s review some helpful
guidelines:
 Be sure to read carefully.
 Define your variable(s)
according to the situation.
 Set-up an equation.
 Solve.
Let’s try one together.
Find two consecutive integers whose sum is 45.
1. Read carefully.
Let x = the first number
Let x + 1 = the second number
2. Define the variables.
x + x + 1 = 45
3. Set up equation.
4. Solve.
2x + 1 = 45
-1
-1
2x = 44
2
The first number is 22, and the
second number is 23.
2
x = 22
x + 1 = 23
Now you try!
Find three consecutive integers whose sum is – 147.
Let’s try another one together.
In the championship game, Chris scored 5 points less than
Dwayne, and LeBron scored 1 point more than twice as many
as Dwayne. If LeBron scored 20 points more than Chris, how
many points were scored by each player?
Let:
Dwayne = x
Chris = x – 5
LeBron = 2x + 1
2x + 1 = x – 5 + 20
2x + 1 = x + 15
-x
-x
x + 1 = 15
-1 -1
In the championship game,
Dwayne scored 14 points,
Chris scored 9 points, and
LeBron scored 29 points.
x = 14
x–5= 9
2x + 1 = 29
Now you try!
The second of three numbers is 8 more than the first, and
the third number is 3 less than 3 times the first. If the third
number is 15 more than the second, find the three numbers.