Lesson 10, Topic 3
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# Sharing Quantities in Given Ratios

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To share quantities in a given ratio:

1. Add the ratios together.
2. Find the fraction of the given ratio that is the total ratio.
3. Use these to multiply the quantity respectively.

To divide quantities into two parts when given a ratio.

### Example 1

Divide ₦120 between Bola and Ade in the ratio 2 : 3

Solution

The given ratio = 2 : 3

Total ratio = 2 + 3 = 5

Bola gets $$\frac{2}{5}\scriptsize \: of \: N120 \\ \scriptsize = 2 \: \times \: 24 = N48$$

Ade gets $$\frac{3}{5}$$of the total amount.

= $$\frac{3}{5}\scriptsize \: of \: N120 \\ \scriptsize = 3 \: \times \: 24 = N72$$

Bola gets ₦48 and Ade gets ₦72.

### Example 2

The ratio of maths books to English books in a library is 15 : 2. The total number of books is 170. Find:

a. the number of maths books
b. the number of English books.

Solution

Ratio =  maths book  :  English book

= 15 : 2

total ratio  =   15 + 2  =  17

The total number of books is 170

a. Number of Maths books

= $$\frac{Maths \; ratio}{Total \; ratio}\scriptsize \: \times \: 170 \\ = \frac{15}{17}\scriptsize \: \times \: 170 \\ \scriptsize 15 \: \times \: 10 = 150 \: Maths \: books$$

b. Number of Maths books

= $$\frac{English \: ratio}{Total \: ratio}\scriptsize \: \times \: 170 \\ = \frac{2}{17}\scriptsize \: \times \: 170 \\ \scriptsize 2 \: \times \: 10 = 20 \: English \: books$$

### Example 3

Two girls shared oranges in the ratio of 3 : 5. The girl with the smaller share got 45 oranges. How many oranges did the other girl get?

Solution

Ratio  =  3 : 5

total  ratio =  3 + 5 = 8

smaller ratio =  3

Let the total number of oranges be x

The girl with smaller ratio gets:

= $$\frac{Smaller \: ratio}{Total \: ratio}\scriptsize \: \times \: x \\ = \frac{3}{8}\scriptsize \: \times \: x \\ \frac{3x}{8} = \frac{45}{1}\\ \scriptsize Cross \: Multiply \\ \scriptsize 3x = 8 \; \times \: 45 \\ \scriptsize Divide \: both \: sides \: by \: 3\\ \frac{3x}{3} = \frac{8 \: \times \: 45}{3}\\ \scriptsize x = 8 \: \times \: 15 = 120$$

120 oranges were shared

The other girl gets:

= $$\frac{5}{8}\scriptsize \: \times \: 120 \\ \scriptsize Divide \: by \: 2\\ \frac{5}{4}\scriptsize \: \times \: 60 \\ \frac{300}{4} \scriptsize = 75 \: oranges$$

Or

The other girl gets (120 – 45)  =  75 oranges

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