USING RATIOS TO DIVIDE QUANTITIES WORD PROBLEMS

Problem 1 :

To make standard concrete, gravel, sand and cement are mixed in the ratio 5 : 3 : 1. I wish to make 18 tonnes of concrete. How much gravel, sand and cement must I purchase?

Solution :

Total parts  =  5 + 3 + 1

  =  9 parts

Quantity of concrete  =  18 tones

Quantity of gravel  =  5/9 of 18

=  (5/9) ⋅ 18

=  10 tonnes of gravel

Quantity of sand  =  3/9 of 18

=  (3/9) ⋅ 18

=  6 tonnes of sand

Quantity of cement  =  1/9 of 18

=  (1/9) ⋅ 18

=  2 tonnes of cement

Problem 2 :

My fortune of $810, 000 is to be divided in the ratio 4 : 3 : 2. How much does each person receive?

Solution :

Let X, Y and Z be three persons.

Total number of parts  =  4 + 3 + 2

=  9 parts

Amount received by X  =  4/9 of 810 000

=  (4/9) ⋅ 810 000

=  360000

Amount received by Y  =  3/9 of 810 000

=  (3/9) ⋅ 810 000

=  270000

Amount received by Z  =  2/9 of 810 000

=  (2/9) ⋅ 810 000

=  180000

Problem 3 :

An alloy is made from copper, zinc and tin in the ratio 17 : 2 : 1. How much zinc is required to make 10 tonnes of the alloy?

Solution :

Total number of parts  =  17 + 2 + 1

=  20 parts

Quantity of Zinc required  =  (2/20) of 10 tonnes

=  (2/20) ⋅ 10

=  1 tonne

Problem 4 :

Joe and Bob share the cost of a video game in the ratio 3 : 7.

a) What fraction does each pay?

b)  If the game costs $35, how much does each pay?

c)  If Joe pays $12, how much does Bob pay?

d)  If Bob pays $42, what is the price of the video game

Solution :

Total parts  =  3 + 7

  =  10 parts

(a)  Joe will pay 3/10 and Bob will pay 7/10.

(b)  Cost of game  =  $35

Joe has to pay  =  (3/10) of 35

=  (3/10) ⋅ 35

=  $10.5

Bob has to pay  =  (7/10) of 35

=  (7/10) ⋅ 35

=  $24.5

c)  Amount paid by Joe  =  3x

3x  =  12

x  =  4

Amount paid by Bob  =  7x

=  7(4) 

=  $28

d) 7x  =  42

x  =  6

Price of video game  =  10x

=  10(6)

=  60

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