# Julia's frogs are 2/5 of the amount of Rimma's frogs. If Rimma gives 1/2 of her frogs to Julia,...

## Question:

Julia's frogs are 2/5 of the amount of Rimma's frogs.

If Rimma gives 1/2 of her frogs to Julia, what will be the ratio of Julia's frogs to Rimma's frogs?

## Ratios:

A ratio is a relation that indicates a comparison between two quantities. It tells us how many times one quantity is contained in another quantity. For example, if a farmer has 20 goats and 40 sheep, then the ratio of goats to sheep is written as {eq}g:s = 20:40 {/eq} which simplifies to {eq}g:s = 1:2 {/eq}.

Let the number of frogs that Rimma has be {eq}x {/eq}. If Julia's frogs are {eq}\dfrac{2}{5} {/eq} of Rimma's frogs, then the expression of Julis's frogs is:

• {eq}\dfrac{2}{5}x {/eq}

If Rimma gives {eq}\dfrac{1}{2} {/eq} of her frogs to Julia, this means that she will be left with {eq}\dfrac{1}{2}x {/eq} and Julia will now have:

• {eq}\dfrac{2}{5}x + \dfrac{1}{2}x = \dfrac{9}{10}x \; \rm frogs {/eq}

The ratio of Julia frogs to Rimma's frogs will be:

• {eq}\dfrac{9}{10}x:\dfrac{1}{2}x {/eq}
• {eq}\dfrac{9}{10}:\dfrac{1}{2} {/eq}

Simplifying the ratio, we get:

• {eq}\boxed{\color{blue}{9:5}} {/eq}