Question

Your club has been asked to contribute to a service project benefiting a local charitable organization. You plan to buy a combination of $5 and $10 gift cards to donate. You plan to buy exactly 20 gift cards and want to spend between $150 and $160. What are the possible combinations of $5 and $10 gift cards your club can purchase? (Write a compound inequality in one variable to solve this problem).

Answer 1

the possible combinations of $5 and $10 gift cards your club can purchase are :

eight $5 gift cards and twelve $10 gift cards

nine $5 gift cards and eleven $10 gift cards

or ten each of $5 gift cards and $10 gift cards

Explanation:

From the information given:

You plan to buy a combination of $5 and $10 gift cards

You plan to buy exactly 20 gift cards and want to spend between $150 and $160.

The objective is to determine the possible combinations of $5 and $10 gift cards your club can purchase?

Let assume the g is the number of the $5 gift cards bought;

then (20 - g) will be the number of the $10 gift card bought.

Thus; the compound inequality for the amount spent between $150 and $160 will be:

= 150 ≤ 5g + 10(20 - g) ≤ 160

= 150 ≤ 5g + 200 - 10g ≤ 160

= 150 ≤ 5g -10 g + 200 ≤ 160

= 150 ≤ -5g + 200 ≤ 160

= 150-200 ≤ -5g ≤ 160 -200

= -50 ≤ -5g ≤ -40

Divide through by -5

= 10 ≥ g ≥ 8

= 8 ≤ g ≤ 10

Thus; the possible combinations of $5 and $10 gift cards your club can purchase are :

eight $5 gift cards and twelve $10 gift cards = i.e 8 ×$5 + 12 ×$10

= $40+$120

=$160

nine $5 gift cards and eleven $10 gift cards

= 9 ×$5 + 11 ×$10

= $45 + $110

= $155

or ten each of $5 gift cards and $10 gift cards

= 10 ×$5 + 10 ×$10

= $50 + $100

= $150

These combinations falls in between the range of $150 and $160.