DIVIDING A QUANTITY IN A GIVEN RATIO

Problem 1:

Divide :

a) $50 in the ratio 1 : 4

b) $35 in the ratio 3 : 4

Solution :

a) We divide the given quantity 50 in the ratio 1 : 4.

Let the first part be x and the second part be 4x.

x + 4x = 50

5x = 50

x = 50/5 ==> 10

1x = 10

4x = 4(10) ==> 40

So, the denominations are 10 and 40 respectively.

b) Let the first and second parts e 3x and 4x respectively.

3x + 4x = 35

7x = 35

x = 35/7

x = 5

3x = 3(5) ==> 15

4x = 4(5) ==> 20

So, the denominations are $15 and $20.

Problem 2 :

A fortune of $800000 is to be divided in the ratio 3 : 7. What is the larger share?

Solution :

Let take first part to be 3x and second part to be 7x.

3x + 7x = 800000

10x = 800000

x = 800000/10

x = 80000

3x = 3(80000) ==> 240000

7x = 7(80000) ==> 560000

So, the largest share is $560000.

Problem 3 :

The ratio of girls to boys in a tennis club is 4 : 5. If there are 144 children in the club, how many are girls?

Solution :

Number of girls = 4x and boys = 5x

4x + 5x = 144

9x = 144

x = 144/9

x = 16

Girls 4x = 4(16)

= 64

So, there are 64 girls in the tennis club.

Problem 4 :

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?

Solution :

Ratio between alcohol to water in the first glass = 1 : 4

Let x be the capacity of the glass.

Quantity of alcohol in 1^st glass = x/5

Quantity of water in 1^st glass = 4x/5

Ratio between alcohol to water in the second glass = 2 : 3

Quantity of alcohol in 2^nd glass = 2x/5

Quantity of water in 2^nd glass = 3x/5

Problem 5 :

One full glass contains vinegar and water in the ratio 1 : 3. Another glass with twice the capacity of the first has vinegar and water in the ratio 1 : 4. If the contents of both glasses are mixed together, what is the ratio of vinegar to water?

Solution :

Let first glass capacity = x

In first glass,

Ratio of vinegar : water = 1 : 3

Second glass capacity = 2x

Vinegar = 1/5 (2x) = 2x/5

Water = 4/5 (2x) = 8x/5

Both glasses capacity = x + 2x = 3x

Vinegar = x/4 + 2x/5

Vinegar = 13x/20

Water = 3x/4 + 8x/5

Water = 47x/20

Ratio of vinegar to water = 13x/20: 47x/20

= 13: 47

Problem 6:

A lemon drink is mixed using one part lemon juice to seven parts water. If 250 ml of lemon juice is used, how much water should be added?

Solution :

Ratio between lemon juice to water = 1 : 7

Quantity o lemon juice = x

Quantity of water = 7x

here x = 250

quantity of water used = 250 (7)

= 1750

So, 1750 parts water should be added.

Problem 7:

At a Falcons vs Crocs basketball match, the ratio of supporters is 5: 3. If there are 4000 in the crowd, how many are Falcons supporters?

Solution :

The ratio of Falcons vs Crocs supporters = 5: 3

Falcons supporters = 5x

Crocs supporters = 3x

5x + 3x = 4000

8x = 4000

x = 4000/8

x = 500

Falcons supporters = 5x

= 5(500)

= 2500

So, 2500 Falcons supporters are in the basketball match.