Answer:
There are 19 quarters and 8 dimes.
Step-by-step explanation:
We will let <em>x</em> denote the amount of quarters.
Since there are 27 coins in total, <em>(27-x) </em>will be the amount of dimes there are.
Since each quarter is worth $0.25, the total value of quarters is given by <em>0.25x.</em>
And since each dime is worth $0.10, the total value of dimes is given by <em>0.1(27-x). </em>
We know that the total value of all 27 coins is $5.55. So, we can write the following equation:
So, we will determine the value of <em>x, </em>the amount of quarters there are.
First, let’s multiply everything by 100 to remove the decimals. So:
Distribute:
Distribute:
Combine like terms:
Subtract 270 from both sides:
Divide both sides by 15:
So, the value of <em>x</em> is 19.
This means that there are 19 quarters.
So, the amount of dimes must be 27-19 or 8 dimes.