WRITING AND SOLVING PROPORTIONS

Problem 1 :

If there are 3 cups of sugar in 24 cookies, how much sugar is there in 72 cookies? Write a proportion.

Solution :

Required ratio will be in the form

cups of sugar : number of cookies

Let x be the quantity of sugar in cups.

3 : 24 = x : 72

Writing ratios as fraction, 

3/24 = x/72

Doing cross multiplication, we get

3(72) = 24x

x = 3(72)/24

x = 9

So, 9 cups of sugar will be there is 72 cookies

Problem 2 :

The word order in some problems requires special care. “A 20-pound turkey serves 28 people. How many people will a 30-pound turkey serve?

Solution :

Number of people served by 20 pound turkey = 28

Number of people served by 30 pound turkey = x

Required ratio will be in the form,

Quantity of turkey : Number of people

20 : 28 = 30 : x

20/28 = 30/x

Doing cross multiplication

20x = 28(30)

x = 28(30) / 20

x = 42

So, 42 people can be served with 30 pounds of turkey.

Problem 3 :

Write a proportion and solve. A biologist determined that there were 42 oak trees in a 5-acre forest. How many oak trees would be expected on 40 acres of identical habitat?

Solution :

Number of oak trees in 5acre forest = 42

Number of oak trees will be in 40 acres forest = x

Ratio will be in the form

Capacity of land : Number of oak trees

5 : 42 = 40 : x

5/42 = 40/x

5x = 40(42)

x = 40(42)/5

x = 336

So, there will be 336 oak trees in 40 acres of land.

Problem 4 :

There are 6 cups of detergent in a bottle. If 1/3 cup is need for 1 load of laundry, how many loads can be cleaned with one bottle of detergent?

Solution :

1/3 of cup is used for 1 load of laundry

6 cups is used for how many loads of laundry.

Let x be the number of loads of laundry.

Ratio will be in the form of,

quantity of cups used : loads of laundry

1/3 : 1 = 6 : x

1/3 / 1 = 6/x

1/3 = 6/x

x = 6(3)

x = 18

So, number of laundry is 18.

Problem 5 :

Write a proportion based on the following information: “The directions on a bottle of fuel additive call for pouring in 12 ounces of additive to each 16 gallons of fuel. How many gallons of fuel will 9 ounces treat?”

Solution :

Number of ounces of additive : Number of gallons of fuel

Let x be the number of gallons of fuel required.

12 : 16 = 9 : x

12/16 = 9/x

12x = 9(16)

x = 9(16)/12

x = 12

Problem 6 :

Susan baked 2 dozen cookies.  If the recipe  called for 3/4 cup of sugar, how much sugar would  she need to bake 4.5 dozen cookies?

Solution :

Let x be the quantity of sugar needed.

Ratio will be in the form of

dozen of cookies : Quantity of sugar

2 : (3/4) = 4.5 : x

2/(3/4) = 4.5/x

8/3 = 4.5/x

Doing cross multiplication

8x = 4.5(3)

x = 13.5/8

x = 1.68

So, 1.68 cups of sugar is needed.

Problem 7 :

Carol can type 660 words in 12 minutes.  How  many words can she type in 40 minutes?

Solution :

Number of words can be typed in 40 minutes be x.

Ratio will be in the form

Number of words types : time given

660 : 12 = x : 40

660/12 = x/40

660(40) = 12x

x = 660(40)/12

x = 2200

So, 2200 words can be typed in 40 minutes.

Problem 8 :

Thirty six pencils are packed in three boxes.   How many pencils are packed in five boxes?

Solution :

Let x be the number of pencils in five boxes.

Ratio will be in the form

number of pencils : number of boxes

36 : 3 = x : 5

36/3 = x/5

36(5) = 3x

x = 36(5)/3

x = 12(5)

x = 60

There will be 60 pencils in 5 boxes.

Problem 9 :

If it costs $13.50 for 5 notebooks, how much will it  cost 8 notebooks?

Solution :

Let x be the cost of 8 notebooks.

Ratio will be in the form

Cost of note books : number of notebooks

13.5 : 5 = x : 8

13.5/5 = x/8

13.5(8) = 5x

x = 13.5(8)/5

x = 21.6

So, cost of 8 note books is $21.6

Problem 10 :

Janet made 48 cookies. She used 1,104 chocolate chips for all of the cookies. How many chocolate chips were in each cookie?

Solution :

Number of chocolate chips in 1 cookie = x

Ratio will be in the form

number of cookies : number of chocolate chips

48 : 1104 = 1 : x

48/1104 = 1/x

48x = 1104

x = 1104/48

x = 23

So, in one cookie, there will be 23 chocolate chips.

Problem 11 :

There are 18,480 feet in 3.5 miles. How many feet are in one mile?

Solution :

Number of feet in 1 mile = x

Ratio will be in the form

number of foot : number of miles.

18480 : 3.5 = x : 1

18480/3.5 = x/1

x = 18480/3.5

x = 5280