Question

Write a word problem that can be represented by the function y = 60 - 2.5x. Find the zero of the function and describe what this value means in the context of the situation.

Answer 1

The function y = 60 - 2.5x can represent a scenario where you have a $60 gift card for a bookshop where each novel costs $2.50. The zero of the function, x = 24, means that you can buy up to 24 novels before the gift card balance reaches $0.

Step-by-step explanation:

Let's create a word problem that corresponds to the function y = 60 - 2.5x. Imagine you have a gift card for a bookshop with $60 and you decide to buy a series of novels, each costing $2.50. Let x represent the number of novels you buy, and y represent the remaining balance on the gift card. The equation y = 60 - 2.5x will help us determine how many books you can buy before the gift card runs out.

To find the zero of the function, we set y to zero and solve for x:

0 = 60 - 2.5x

2.5x = 60

x = 60 / 2.5

x = 24

The zero of the function is at x = 24. This means if you buy 24 novels, your gift card balance will be depleted to $0. This zero gives us the maximum number of novels you can purchase with your gift card.