Problem Statement:

**A cook can cook 4 large cakes in an hour. **

**A cook can cook 12 small cakes in an hour.**

**A kitchen is available for two hours for cooks to use.**

**How many cooks will it take to cook 29 large cakes and 220 small cakes in the kitchen?**

Let X = the number of cooks it takes to cook 29 large cakes and 220 small cakes in 2 hours.

This can be considered as two separate problems added together:

L = number of cooks to cook 29 large cakes in 2 hours.

S = number of cooks to cook 220 small cakes in 2 hours.

X = L + S

**Part 1: **

How many cooks will it take to cook 29 large cakes in 2 hours?

Let L = number of cooks to cook 29 large cakes in 2 hours.

A cook can cook 4 large cakes in an hour.

Let rate l = 4 *(units = large cakes cooked/cook*hour)*

**Write an** **equation **for this part of the problem:

29 = L * 2 * l

Look at the units on both sides of the = sign. They should be the same.

29* (large cakes cooked) *= L* (cooks) ** 2* (hours) ** l* (large cakes cooked/cook*hour)*

**Solve for L:**

Replace l with 4

29 = L * 2 * 4

Divide both sides of the = sign by 2 * 4 = 8 and switch the left and right sides of the = sign.

L = 29/8 > 3

**L = 4 cooks**

**Part 2:**

How many cooks will it take to cook 220 small cakes in 2 hours?

Let S = number of cooks to cook 29 large cakes in 2 hours.

A cook can cook 12 small cakes in an hour.

Let rate s = 12* (units = small cakes cooked/cook*hour)*

Write an equation for this part of the problem:

220 = S * 2 * s

Look at the units on both sides of the = sign

220* (small cakes cooked)* = S *(cooks)** 2 *(hours)* * s *(small cakes cooked/cook*hour)*

Replace s with 12

220 = S * 2 * 12

Divide both sides of the = sign by 2 *12 = 24 and switch the left and right sides of the = sign.

S = 220/24 > 9

**S = 10 cooks **

Solve for X

X = L + S = 4 + 10

**X = 14 cooks**