Lily and nada share silver coins in the ratio 7:3. if lily gives 3 silver coins to nada, the ratio becomes 5:3. how many silver coins did lily have initially?

A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.

The first is a part-to-part ratio, and the second is a part-to-whole ratio.
The part-to-part ratio expresses the relationship between 2 separate entities or groups.

Now according to the question;

Let 'x' be the share of silver coin of Lily.

Let 'y' be the share of silver coin of Nada.

Lily and Nada share silver coins in the ratio 7:3

Thus, x/y = 7/3

Cross-multiplying

3x = 7y (equation 1)

Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.

(x - 3)/(y + 3) = 5/3

cross multiplying;

3x - 9 = 5y + 15

Simplifying;

3x = 5y + 24 (equation 2)

Comparing equation 1 and 2.

7y = 5y + 24

2y = 24

y = 12 (Nada's share)

Substitute the value of y in equation 1;

3x = 7y

3x = 7×12

x = 28

Therefore, the initial share if Lily was 28.

To know more about the ratios, here

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