FINDING THE MISSING NUMBERS IN AN EQUIVALENT RATIOS

Find x if :

Problem 1 :

2 : 5 = 8 : x

Solution :

Let ‘x’ be the unknown.

2 : 5 = 8 : x

If two ratios are equal, then

Product of extremes = Product of means

2 ⋅ x = 5 ⋅ 8

2x = 40

x = 40/2

x = 20

So, the missing numbers is 20.

Problem 2 :

3 : 7 = x : 21

Solution :

Let ‘x’ be the unknown.

3 : 7 = x : 21

If two ratios are equal, then

Product of extremes = Product of means

3 ⋅ 21 = 7 ⋅ x

63 = 7x

63/7 = x

9 = x

So, the missing numbers is 9.

Problem 3 :

4 : 5 = 16 : x

Solution :

Let ‘x’ be the unknown.

4 : 5 = 16 : x

If two ratios are equal, then

Product of extremes = Product of means

4 ⋅ x = 5 ⋅16

4x = 80

x = 80/4

x = 20

So, the missing numbers is 20.

Problem 4 :

2 : 6 = x : 27

Solution :

Let ‘x’ be the unknown.

2 : 6 = x : 27

If two ratios are equal, then

Product of extremes = Product of means

2 ⋅ 27 = 6 ⋅ x

54 = 6x

54/6 = x

9 = x

So, the missing numbers is 9.

Problem 5 :

12 : 9 = 16 : x

Solution :

Let ‘x’ be the unknown.

12 : 9 = 16 : x

If two ratios are equal, then

Product of extremes = Product of means

12 ⋅ x = 9 ⋅16

12x = 144

x = 144/12

x = 12

So, the missing numbers is 12.

Problem 6 :

15 : 25 = 9 : x

Solution :

Let ‘x’ be the unknown.

15 : 25 = 9 : x

If two ratios are equal, then

Product of extremes = Product of means

15 ⋅ x = 25 ⋅ 9

15x = 225

x = 225/15

x = 15

So, the missing numbers is 15.

Problem 7 :

A hospital employs nurses and doctors in the ratio 7 : 2. If there are 84 nurses, how many doctors are there?

Solution :

Ratio of nurses to doctors

= 7 : 2

Ratio between nurses to doctors, when nurses are 84.

Let ‘x’ be the number of doctors.

7 : 2 = 84 : x

7 ⋅ x = 84 ⋅ 2

7x = 168

x = 168/7

x = 24

So, 24 doctors are there.

Problem 8 :

A farmer has pigs and chickens in the ratio 3 : 8. If she has 360 pigs, how many chickens does she have?

Solution :

Ratio of pigs and chickens

= 3 : 8

Ratio between pigs to chickens, when pigs = 360.

Let ‘x’ be the number of chickens.

3 : 8 = 360 : x

3 ⋅ x = 360 ⋅ 8

3x = 2880

x = 2880/3

x = 960

So, 960 chickens does she have.

Problem 9 :

The price of a TV is reduced from $500 to $400. A DVD player costing $1250 is reduced in the same ratio as the TV. What does the DVD player sell for?

Solution :

Let the DVD player sell for x.

The price of a TV is reduced from $500 to $400.

A DVD player costing $1250 is reduced in the same ratio as the TV.

500 : 400 = 1250 : x

500x = 400(1250)

x = (400/500) ⋅ (1250)

x = 1000

So, the DVD player sell for 1000.