you have been asked to contribute to a service project benefiting a local organization. you plan to buy a combination of $5 dollar and $10 gift cards to donate.

Question

you have been asked to contribute to a service project benefiting a local organization. you plan to buy a combination of $5 dollar and $10 gift cards to donate. You plan to buy exactly 20 gift cards and want to spend between $150 and $160. What ar the possib,e combinations of $5 and $10 gift cards you can purchase? write a compound inequality in one variable to solve this problem

Answer 1

If x = the number of $5 gift cards purchased, then (20 - x) = the number of $10 gift cards purchased

 

The compound inequality would be set up as the following:

 

150 ≤ 5x + 10(20 - x) ≤ 160

 

150 ≤ 5x + 200 - 10x ≤ 160

 

150 ≤ 200 - 5x ≤ 160

 

-50 ≤ -5x ≤ -40

 

10 ≥ x ≥ 8

 

8 ≤ x ≤ 10

 

You could buy eight $5 and twelve $10 gift cards

 

or nine $5 gift cards and eleven $10 gift cards

 

or ten each of $5 and $10 gift cards