Question

a cake machine needs to be programmed to make cakes. the cake recipe requires 5 cups of sugar to make 4 cakes.
a. what is the constant of proportionality?
b. write an equation to model the cups of sugar, s, for any number of cakes, c.
c. how many cups of sugar are needed to bake 24 cakes?

Explanation:

Part (a)

Step1: Recall constant of proportionality formula

The constant of proportionality \( k \) in a proportional relationship \( y = kx \) (here, sugar \( s \) and cakes \( c \) are proportional, so \( s=kc \)) is found by \( k=\frac{s}{c} \).
Given \( s = 5 \) cups when \( c = 4 \) cakes, so \( k=\frac{5}{4} \).

Step1: Use proportional relationship formula

Since \( s \) (sugar) and \( c \) (cakes) are proportional, \( s=kc \), and from part (a) \( k = \frac{5}{4} \).
So the equation is \( s=\frac{5}{4}c \).

Step1: Substitute \( c = 24 \) into the equation

We have the equation \( s=\frac{5}{4}c \). Substitute \( c = 24 \): \( s=\frac{5}{4}\times24 \).

Step2: Calculate the value

\(\frac{5}{4}\times24 = 5\times6 = 30\).

Answer:

\(\frac{5}{4}\)

Part (b)