Question

A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?

Answer 1

$\text{rate}_{wekly}=\frac{35}{3}\text{slices per w}eek$

Explanation

to find the weekly rate of eating we need to use

$\text{rate}_{wekly}=\frac{eaten\text{ slices}}{\nu\text{mber of we}eks}$

hence, we need to convert 3 days into weeks, ( let x represents the number of weeks in 3 days),so

1 week= 7 days

x weeks= 3 days

the proportion is

$\begin{gathered} \frac{1\text{ w}eek}{7\text{ days}}=\frac{x\text{ w}eeks}{3\text{ days}} \\ \frac{1}{7}=\frac{x}{3} \\ \text{Multiply both sides by 3} \\ \frac{1}{7}\cdot3=\frac{x}{3}\cdot3 \\ \frac{3}{7}=x \end{gathered}$

therefore

$3\text{ days=3/7 of w}eek$

Now, replace .

$\begin{gathered} \text{rate}_{wekly}=\frac{eaten\text{ slices}}{\nu\text{mber of we}eks} \\ \text{rate}_{wekly}=\frac{5\text{ slices}}{\frac{3}{7}\text{ we}ek} \\ \text{rate}_{wekly}=\frac{35\text{ slices}}{3\text{ w}eks} \\ \text{rate}_{wekly}=\frac{35}{3}\text{slices per w}eek \end{gathered}$

I hope this helps you