Question

a baker is packing cookies into gift boxes. she places the same number of cookies in each box. after packing 12 boxes, she has 324 cookies left. after packing 35 boxes, she has 25 cookies left.
complete the equation that describes the relationship between the number of cookies remaining, c, and the number of boxes packed, p.
write your answer using whole numbers or decimals rounded to the nearest tenth.
c = \boxed{} p + \boxed{}

Explanation:

Step1: Find the slope (cookies per box)

The slope \( m \) is the change in \( C \) over change in \( p \).
Change in \( C \): \( 25 - 324 = -299 \)
Change in \( p \): \( 35 - 12 = 23 \)
\( m = \frac{-299}{23} \approx -13.0 \)

Step2: Find the y-intercept (total cookies)

Use \( C = mp + b \), plug in \( p = 12 \), \( C = 324 \), \( m = -13 \):
\( 324 = -13(12) + b \)
\( 324 = -156 + b \)
\( b = 324 + 156 = 480 \)

Answer:

\( C = -13.0p + 480 \)