Question

Allison’s cupcake and cookie budget for her party are $105. She would like to have at least 40 cupcakes and cookies combined and would like to have at most 5 more cupcakes than cookies. If cupcakes sell for $2.50 and cookies for $1.50, which system of inequalities could help Allison determine possible numbers of cupcakes (a) and cookies (b) that she should buy?
(
a
≥
0
,
b
≥
0
)

Answer 1

The system of Inequalities that represents the possible number of cupcakes and cookies that Allison should buy is;

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

• We are told she desires to have at least 40 cupcakes and cookies combined.

We are told that;

a is the number of cupcakes

b is the number of cookies

Then this inequality is written as;

a + b ≥ 40

• Secondly, we are told she desires to have at most 5 more cupcakes than cookies.

Thus, the inequality would be;

a + 5 ≤ b

• Thirdly, we are told that cupcakes sell for $2.50 and cookies for $1.50

Therefore, the inequality is;

2.50a + 1.50b ≤ 105

In total, the 3 inequalities would be;

a + b ≥ 40

a + 5 ≤ b

2.50a + 1.50b ≤ 105

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