Answer:
Herlene has 8 dimes and 17 quarters
Explanation:
System of Equations
Let's call:
x = number of dimes Herlene has
y = number of quarters Herlene has
Since each dime has a value of $0.10 and each quarter has a value of $0.25, the total money Herlene has is 0.10x+0.25y.
We know this amount is $5.05, thus:
0.10x + 0.25y = 5.05 [1]
It's also given the number of quarters is one more than twice the number of dimes, i.e.:
y = 2x + 1 [2]
Substituting in [1]:
0.10x + 0.25(2x + 1) = 5.05
Operating:
0.10x + 0.5x + 0.25 = 5.05
0.6x = 5.05 - 0.25
0.6x = 4.8
x = 8
From [2]:
y = 2*8 + 1 = 17
y = 17
Herlene has 8 dimes and 17 quarters