Answer:
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
Step-by-step 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.
