SOLVING RATIO AND PROPORTION WORD PROBLEMS

Set up a proportion to solve each problem, show all work, and label all answers.

Problem 1 :

The ratio of boys is 3 to 2. If there are 12 boys, how many girls are there?

Solution:

Let x be the number of girls.

3 : 2 = 12 : x

Therefore, there are 8 girls.

Problem 2 :

It takes one Super Giant Pizza to feed 3 people. If you invite 36 people, how many pizzas will you need?

Solution:

Let x be the pizzas.

1 : 3 = x : 36

So, we will need 12 super giant pizzas to feed 36 people.

Problem 3 :

At a recent party, it cost $9.50 for refreshments for 10 guests. At this rate, how much would it cost to have refreshments for 80 guests?

Solution:

Let x be the cost.

9.50 : 10 = x : 80

So, it would cost $76 to have refreshments for 80 guests.

Problem 4 :

Mary has saved $17.50 in the past 3 weeks. At this rate, how much will she save in 15 weeks?

Solution:

17.50 : 3 = x : 15 

So, she will have saved $87.50.

Problem 5 :

Mr. Johnson was paid $190 for a job that required 40 hours of work. At this rate, how much should he be paid for a job requiring 60 hours of work?

Solution:

190 : 40 = x : 60

So, at the same rate, he should be paid $285 for 60 hours of work.

Problem 6 :

The park ranger stocks the children's fishing pond keeping a ratio of  4 sunfish to 3 perch. If he puts 300 sunfish into the pond, how many perch should be put into the pond?

Solution:

Let x represents the number of perch in the pond.

4 : 3 = 300 : x

There should be 225 perch put in the pond.

Problem 7 :

If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13 people?

Solution:

Let x be the pounds.

2 : 5 = x : 13

So, 5.2 pounds will be needed to serve 13 people.

Problem 8 :

Jack was planting a tree. He was to dig a hole that was 3 feet deep for every 5 feet of tree height. How deep should he dig the hole for a tree that is 17 feet high?

Solution:

Let x represents the depth of the hole.

3 : 5 = x : 17 

So, the hole should be 10.2 feet deep. 

Problem 9 :

A certain shade of green paint is made from 5 parts yellow mixed with three parts blue. If 2 cans of yellow are used, how many cans of blue should be used?

Solution:

Let x be the blue paint.

5 : 3 = 2 : x 

So, 1.2 cans of blue should be used.

Problem 10 :

If a 4-pound roast takes 150 minutes to cook, how long should a five-pound roast take?

Solution:

Let x represent the time needed to roast 5-pound roast.

4 : 150 = 5 : x

So, a 5-pound roast should take approximately 187.5 minutes to cook.