WRITING AND SOLVING PROPORTIONS WORD PROBLEMS 

Problem 1 :

A jar of peaches weighs 13 ounces. There are 16 jars in a crate. How many ounces does a crate weigh?

Solution :

Quantity of peaches in 1 jar = 13 ounces.

Number of jars in crate  = 16

Quantity of peaches in 16 jars = x

Ratio will be in the form,

quantity of peaches : number of jars

1 : 13 = 16 : x

1/13 = 16/x

Doing cross multiplication, we get

x = 13(16)

x = 208

208 ounces of peaches in 16 jars.

Problem 2 :

Tonya drove 343 miles the first day of her trip. How many days will it take her to drive the remaining 1,200 miles if she continues at the same rate?

Solution :

Distance covered in 1 day of trip = 343 miles

Number of days will be taken to cover 1200 miles = x

1 : 343 = x : 1200

1/343 = x/1200

1200 = 343x

x = 1200/343

x = 3.49

Approximately 3.5 days will be needed to cover 1200 miles.

Problem 3 :

A 6-pound ham will serve 14 people. How many people will a 9-pound ham serve? Set up a proportion and solve.

Solution :

6 pounds of ham will be served for 14 people

Number of people will be served with 9 pound ham = x

Ratio will be in the form

number of pounds of ham : number of people get served

6 : 14 = 9 : x

6/16 = 9/x

6x = 16(9)

x = 144/6

x = 24

9 pounds of ham will be served for 24 people.

Problem 5 :

A fine fabric was selling for $ 10.50 a yard. Joni bought 2 1/3 yards. How much did she spend?

Solution :

Cost of 1 yard of fabric = 10.50

Cost of 2 1/3 yards of fabric = x

1 : 10.50 = 2  1/3 : x

1 : 10.50 = 7/3 : x

1/10.50 = 7/3x

3x = 10.50(7)

x = 10.50(7)/3

x = 24.5

He has to spend $24.5 for 2 1/3 yards of fabric.

Problem 6 :

A doctor’s orders are to give his patient 250 milligrams of a pain-relieving medication. If there are 50 milligrams in a capsule, then how many capsules should the patient take?

Solution :

1 capsule will contain 50 milligrams.

How many capsules will contain 250 milligrams of drug.

Let x be the number of capsules.

1 : 50 = x : 250

1/50 = x/250

250 = 50x

x = 250/50

x = 5

5 capsules will contain 250 milligrams of drug.

Problem 7 :

You have 18 days to complete your math prescription in order to retake the Test of Adult Basic Education (TABE). You’ve noticed that it takes you 2 days to finish 7 modules, but there are still 24 modules left to do. How many days will it take to finish? Will you finish on schedule?

Solution :

In 2 days, we can finish 7 module.

Number of modules to be completed = 24

Number of days required for that = x

2 : 7 = x : 24

2/7 = x/24

24(2) = 7x

x = 24(2) / 7

x = 48/7

x = 6  6/7 days

Total number of days will be taken = 2 + 48/7

= 62/7

= 8.85

So, we can finish it in 8.85 days.

Problem 8 :

The next-door neighbors are spending 10 hours a week maintaining their ½ acre property. You are thinking about landscaping your own property in exactly the same way, but it is a 1/3 acre lot. How many hours per week will you have to spend maintaining your property?

Solution :

Let x be the number of hours taken to maintain 1/3 acre land.

Ratio can be written in the form,

number of hours taken : amount of land

10 : 1/2 = x : 1/3

10/(1/2) = x/(1/3)

20 = 3x

x = 20/3

x = 6.6 hours

So, he has to spend 6.6 hours for 1/3 acre of land.

Problem 9 :

A piece of stone on Planet Y weighs seven pounds, but on Earth it weighs only 4 pounds. What would a 130-pound Earthling weigh on Planet Y?

Solution :

Ratio will be in the form of,

weight of stone in planet Y : weight in Earth

Let x be the weight of stone in planet Y, when its weight is 130 pound in Earth.

7 : 4 = x : 130

7/4 = x/130

7(130) = 4x

x = 7(130)/4

x = 227.5 pounds

Weight of the stone at planet Y is 227.5 pounds when its weight is 130 pounds in Earth.

Problem 10 :

Eighty-eight percent of all people who try to do this ratio and proportion worksheet find they need some help with the problems. There are now 49 people who have asked for help while doing this worksheet. How many people have worked on this worksheet so far?

Solution :

Out of 100, 88 people are looking for help.

Now 49 people are looking for help, let x be the required number of people working on the worksheet.

100 : 88 = x : 49

100/88 = x/49

100(49) = 88x

x = 55.68

So, 56 people are looking for help.

Problem 11 :

Write a proportion based on the following information: “A new energy efficient car travels 720 miles on 12 gallons of gas. How many gallons would be used on a 1000 mile trip?”

Solution :

Required ratio will be 

number of miles travelled : quantity of gas used

Let x be the quantity of gas used for 1000 mile trip.

720 : 12 = 1000 : x

720/12 = 1000/x

720x = 12(1000)

x = 12(1000)/72

x = 166.6 gallons

So, 167 gallons of gas should be used for 1000 mile trip.