Victoria is counting all of quarters and dimes from the family piggy bank for the month. If there are 12 times as many dimes are there are quarters, and the total change is worth $21.75, how many quarters and how many dimes were in the piggy bank

Let number of quarters in family piggy bank = x

Let number of dimes in family piggy bank = y

Given that "there are 12 times as many dimes are there are quarters". so we can write equation:

y=12x ... (i)

Given that " total change is worth $21.75".

We know that 1 quarter = $0.25 and 1 dime = $0.10

So other equation will be:

0.25x+0.10y=21.75 ... (ii)

Now we just need to solve both equations.

Plug (i) into (ii)

0.25x+0.10y=21.75

0.25x+0.10 (12x) = 21.75

0.25x+1.2x=21.75

1.45x=21.75

x=15

plug x=15 into (i)

y=12x=12*15=180

Hence final answer is given as:

Number of quarters in family piggy bank = 15

Number of dimes in family piggy bank = 180