Question

1. open response daniella makes apple pies each fall. the cost at the local grocery store for x pounds of apples is shown in the table. what is the least amount of money daniella will spend for 15 pounds of apples? assume the relationship is proportional. (lesson 9)

number of pounds, x | total cost ($), y
2 | $4.50
3 | $6.75

Explanation:

Step1: Find the unit rate

Since the relationship is proportional, the unit rate (cost per pound) can be found by dividing the total cost by the number of pounds. For \( x = 2 \) pounds and \( y=\$4.50 \), the unit rate \( r=\frac{y}{x}=\frac{4.50}{2} = 2.25 \) dollars per pound. We can check with the other data point: for \( x = 3 \) pounds and \( y = 6.75 \) dollars, \( r=\frac{6.75}{3}=2.25 \) dollars per pound. So the unit rate is consistent.

Step2: Calculate the cost for 15 pounds

To find the total cost \( y \) for \( x = 15 \) pounds, we use the proportional relationship \( y=rx \), where \( r = 2.25 \) and \( x = 15 \). So \( y=2.25\times15 = 33.75 \) dollars.

Answer:

\( \$33.75 \)