Answer:
There are 12 dimes and 15 quarters.
Explanation:
Pick a variable to stand for the number of dimes and another variable to stand for the number of quarters. The amount of money you have in dimes is 10 times the variable. I left the decimal off on purpose because we can just think of it as cents and its less stressful if math is already challenging. The amount of money you have in quarters is 25 times the variable for quarters.
x = number of dimes
y = number of quarters
10x is amount of money in dimes.
25y is the amount of money in quarters. Write two separate equations based on the fact that there are 27 coins: x + y = 27.
And,
10x + 25y = 495
(remember we left out the decimal on purpose).
See image to solve by elimination. You could also solve by substitution or matrix work, but I just did substitution. See image.