Question

Arlene wants to buy cakes costing $9 each and pies costing $12 each, with a budget of $48. Let c represent the number of cakes and p represent the number of pies. The inequality representing this situation is:

9c+12p≤48

determine if Arlene can purchase 3 cakes, substitute c=3 into the inequality and evaluate:

a. 9(3)+12p≤48

b. 27+12p≤48

c. 12p≤21

d. p≤1221​

Answer 1

After evaluating the inequality 9c + 12p ≤ 48 with c = 3, we find that Arlene can purchase a maximum of 1 pie after buying 3 cakes with her $48 budget.

Step-by-step explanation:

The inequality representing Arlene's budget when buying cakes costing $9 each and pies costing $12 each with a budget of $48 is 9c + 12p ≤ 48. To determine if Arlene can purchase 3 cakes, we substitute c = 3 into the inequality:

• 9(3) + 12p ≤ 48 which simplifies to
• 27 + 12p ≤ 48, and then by subtracting 27 from both sides we get
• 12p ≤ 21. To find the maximum value of p that satisfies this inequality, we divide both sides by 12, resulting in
• p ≤ 21/12 which simplifies to
• p ≤ 1.75

Since Arlene cannot purchase fractional pies, the maximum number of pies she can buy after purchasing 3 cakes is 1 pie.