Question

Write a linear inequality to represent the information given. Shanley would like to give $5 gift cards and $8 teddy bears as party favors. Shanley has $136 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution and show how your solution works for your inequality.

Answer 1

5c + 8b < = 136 Where c = gift cards and b = teddy bears.

Subtract 8b from both sides
5c < = -8b + 136
Divide both sides by 5
c < = -8/5 b + 136/5
c < = -1.6b + 27.2
c < = -1.6(7) + 27.2
c < = -11.2 + 27.2
c = 16
Gift cards 16
Teddy bears 7
(7, 16)

Answer 2

`5x+8y\leq 136`

Solution:(6,13)

Explanation:

We are given that

Cost of 1 gift card=$5

Cost of 1 teddy bear=$8

Shanley has money to spend on party favors=$136

Number of gift cards=x

Number of teddy bears=y

We have to find the linear inequality to represents the given information.

According to question

`5x+8y\leq 136`

Subtracting 5x on both sides

`8y\leq 136-5x`

Divided by 8 on both sides then, we get

`y\leq (136-5x)/(8)`

Substitute x=6

Then, we get

`y\leq (136-5(6))/(8)=13.25`

`y\leq 13.25`

Number of teddy bears=13

Number of gift cards=6

`5(6)+13(8)=134` <136

Point (6,13) satisfied the inequality.

Therefore, the solution of given inequality is (6,13).