Variables
x: number of dimes
y: number of quarters
If she has 27 coins, then:
x + y = 27
Each dime is worth $0.1, each quarter is worth $0.25. All together the coins are worth $3.45, then:
0.1x + 0.25y = 3.45
Isolating x from the first equation:
x = 27 - y
Substituting this into the second equation:
0.1(27 - y) + 0.25y = 3.45
0.1*27 - 0.1y + 0.25y = 3.45
2.7 + 0.15y = 3.45
0.15y = 3.45 - 2.7
0.15y = 0.75
y = 0.75/0.15
y = 5
And the value of x is:
x = 27 - 5
x = 22
She has 22 dimes and 5 quarters