Answer:
She has 11 quarters and 2 dimes.
Explanation:
Let the amount of quarters = q
And the amount of dimes = d
We can write 2 equations with the given information.
q + d = 13 --- amount of quarters plus amount of dimes = 13 coins
0.1d + 0.25q = 2.95 --- a time is 0.1 dollars and a quarter is 0.25 dollars each
Now we can solve for both values as a system of equations.
q + d = 13
q = 13 - d --- subtract d from both sides to get q by itself
0.1d + 0.25(13 - d) = 2.95 --- substitute in our new value for q into the other equation so we only have 1 variable
0.1d + 3.25 - 0.25d = 2.95 --- distribute 0.25
-0.15d + 3.25 = 2.95 --- combine like terms
-0.15d = -0.3 --- subtract 3.25 from both sides
d = 2 --- divide both sides by -0.15
Now we can go back to the first equation because we know what d is.
q + 2 = 13
q = 11 --- subtract 2 from both sides.
She has 11 quarters and 2 dimes.
0.1d + 0.25q = 2.95
0.1(2) + 0.25(11)
0.2 + 2.75
2.95 = 2.95
Answer is correct.