Lesson 10, Topic 3
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# Sharing Quantities in Given Ratios

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To share quantities in a given ratio:

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 N120 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 N48 and Ade gets N72.

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 error: