How many cooks will it take to cook 29 large cakes and 220 small cakes in a kitchen that is available for 2 hours?

Question

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?

Answer 1

I believe this is a rate problem.

A cook can cook 4 large cakes in an hour.  - (therefore, in 2 hours 1 cook can do 8 cakes

A cook can cook 12 small cakes in an hour. - (therefore, in 2 hours 1 cook can do 24 cakes)

Assuming you cannot slip a cook's time to do both a small and large portion of a cake..... you would take the number of cakes needed and divide by the number they can get done in the 2 hour window. So...

1. 29(large)/8 = 3.625 cooks (let's call this 4 cooks)
2. 220(small)/24 = 9.16 cooks (let's call this 10 cooks)
3. so a total of 14 cooks are needed to complete 29 large and 220 small cakes in 2 hours.

I hope this helps you understand the problem! :-)

Answer 2

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