Do Now

Use the information in the table to determine whether the rule works for thegiven input-output pair. Write “Yes” if the rule works for the input-output pairand “No” if it does not. Write the rule that works for all pairs.

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

apple e

egg g

hour r

and d

eight t

Input Output

sing 16

chair 25

is 4

a 1

revolve 49

Modeling Using Equations

Let’s look for more rules!!!Find a rule for each input-output table. State your rule intwo different ways: (1) as a sentence; and (2) as an equation.

x Process y

-0.5 7.5

0 8

0.5 8.5

1 9

1.5 9.5

x Process y

0 7

3 4

5 2

-5 12

-1 8

Link to the Real WorldMia 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 thenumber of CDs ordered, C, to the payment amount, P.

C Process P

3 25

Rule:

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. Rightnow, Romero’s score is 11 less than 2 times Nelson’s score. For example, if Nelson has 80 points, than Romero has 149 points. Findfour more possibilities for the brothers’ scores and fill in the table below. Then write a rule relating Romero’s score, R, to Nelson’sscore, N.

N Process R

80 149

Rule:

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 amountfor 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.

Let x = the first number

Let x + 1 = the second number2. Define the variables.

x + x + 1 = 453. Set up equation.

1. Read carefully.

4. Solve.

2x + 1 = 45

- 1 - 1

2x = 44

2 2

x = 22

x + 1 = 23The first number is 22, and the second number is 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 thanDwayne, and LeBron scored 1 point more than twice as manyas Dwayne. If LeBron scored 20 points more than Chris, howmany points were scored by each player?

Let:Dwayne = xChris = x – 5LeBron = 2x + 1

2x + 1 = x – 5 + 20

2x + 1 = x + 15- x - x

x + 1 = 15- 1 - 1

x = 14

x – 5 = 9

2x + 1 = 29

In the championship game,Dwayne scored 14 points, Chris scored 9 points, andLeBron scored 29 points.

Now you try!

The second of three numbers is 8 more than the first, andthe third number is 3 less than 3 times the first. If the thirdnumber is 15 more than the second, find the three numbers.