Question 660238
x = # of nickels
y = # of dimes

x + y = 207
.05x + .1y = 17.55

Multiply the first equation by -.05 and add the second equation
-.05(x+y=207)
-.05x - .05y = -10.35

-.05x + .05x - .05y + .1y = -10.35 + 17.55
Combine like terms
.05y = 7.2
.05y/.05 = 7.2/.05
y = 144 dimes

Plug into first equation
x + 144 = 207
x = 207 - 144
x = 63 nickles

Proof
(.1)144 = 14.40
(.05)63 = 3.15
14.40+3.15=17.55