Question

Hannah has a budget of $70 for food at her party. She spent $34 on sushi and drinks. Cupcakes cost $1.75 each. The inequality below can be used to determine the number of cupcakes, c, that Hannah can buy: 34 + 1.75c < 70. Which statement below is true?

1) Hannah can buy a minimum of 20 cupcakes.
2) Hannah can buy a maximum of 21 cupcakes.
3) Hannah can buy a minimum of 21 cupcakes.
4) Hannah can buy a maximum of 20 cupcakes.

Answer 1

Solving the inequality 34 + 1.75c < 70, Hannah can spend $36 on cupcakes after spending $34. Dividing $36 by the cost per cupcake, $1.75, yields approximately 20.57, meaning Hannah can buy a maximum of 20 cupcakes.

Step-by-step explanation:

To determine the number of cupcakes, c, that Hannah can buy, we can solve the inequality 34 + 1.75c < 70. Starting with subtraction, we take away the amount already spent on sushi and drinks from Hannah's total budget:

• 70 - 34 = 36

Now, we divide the remaining budget by the cost of one cupcake:

• 36 / 1.75 ≈ 20.57

Since Hannah can't buy a fraction of a cupcake, she can only buy a whole number of cupcakes. Therefore, Hannah can buy a maximum of 20 cupcakes since 21 would exceed her budget, making the correct statement option 4).