Chapter 3.2, Problem 24E

Reminder Round all answer to two decimal places unless otherwise indicated.

Budget Constraints Your family likes to eat fruit, but because of budget constraints, you spend only $\$5$ each week on fruit. Your two choices are apples and grapes. Apples cost $\$1$ per pound, and grapes cost $\$2$ per pound. Let $a$ denote the number f pounds of apples you buy and $g$ the number of pounds of grapes. Because of your budget, it is possible to express $g$ as a linear function of the variable $a.$ To find the linear formula, we need to find its slope and initial value.

a. If you buy one more pound of apples, how much less money do you have available to spend on grapes? Then how many fewer pounds of grapes can you buy?

b. Use your answer to part a to find the slope of $g$ as a linear function of $a.$ (Hint: Remember that the slope is the change in the function that results from increasing the variable by $1.$ Should the slope of $g$ be positive or negative?)

c. To find the initial value of $g,$ determine how many pounds of grapes you can buy if you buy no apples.

d. Use your answer to parts $\text{b}$ and $\text{c}$ to find a formula for $g$ as a linear function of $a.$