# The ratio of quarters to dimes in a coin collection is 5:3. You add the same number of new quarters as dimes to the collection. Is the ratio of quarters to dimes still 5:3?

No

#### Explanation:

Let's do it this way - let's start with 5 Quarters and 3 Dimes. I'll write it this way:

$\frac{Q}{D} = \frac{5}{3}$

and now we add some coins. I'll add 15 to each pile, which gives us:

$\frac{5 + 15}{3 + 15} = \frac{20}{18}$

Is $\frac{5}{3} = \frac{20}{18}$?

$\frac{20}{18} = \frac{10}{9} \cong \frac{3.333}{3}$

And so no, the ratio didn't stay the same:

$\frac{5}{3} \ne \frac{3.333}{3}$