Answer:
Step-by-step explanation:
The given relations can be used to write two equations describing the coins. One equation can express the total number of coins; the other, their total value.
__
<h3>setup</h3>
Let d and q represent the numbers of dimes and quarters, respectively. The the total number of coins is ...
d + q = 25
and their total value is ...
0.10d +0.25q = 5.20
<h3>solution</h3>
Using the first equation to write an expression for d, we can substitute that into the second equation.
d = 25 -q
0.10(25 -q) +0.25q = 5.20
0.15q = 2.70 . . . . . . . . . collect terms, subtract 2.50
q = 18 . . . . . . . . . . . divide by 0.15
d = 25 -q = 7
You have 18 quarters and 7 dimes.
_____
<em>Additional comment</em>
It is generally convenient to solve for the number of the higher-value coin. That way, the numbers in the equations stay positive, tending to reduce errors.
