Number of dimes are 18 and number of quarters are 31
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
A collection of dimes and quarters is worth $9.55
value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55
0.10d + 0.25q = 9.55 ---------- eqn 1
If the quarters were dimes and the dimes were quarters, the total value would be 7.60
quarters were dimes means , q = d
dimes were quarters means d = q
0.25d + 0.10q = 7.60 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find "d" and "q"
Multiply eqn 1 by 2.5
0.25d + 0.625q = 23.875 ---- eqn 3
Subtract eqn 2 from eqn 3
0.25d + 0.625q = 23.875
0.25d + 0.10q = 7.60
( - ) ----------------------
0.525q = 16.275
q = 31
Substitute q = 31 in eqn 1
0.10d + 0.25q = 9.55
0.10d + 0.25(31) = 9.55
0.10d + 7.75 = 9.55
0.10d = 1.8
d = 18
Thus dimes are 18 and number of quarters are 31