Question 771765
Dimes = x
Quarters = y
x + y = 100.....1
10x + 25y = 1975....2
Multiply Eq (1) by 25
25x + 25y = 2500....3
10x + 25y = 1975....2
Subtract (2) from (3)
15x        = 525
x         = 35
Substitute x = 35 into Eq (1)
x + y = 100
35 + y = 100
y = 100 - 35
y = 65.
Therefore there are 35 dimes and 65 quarters.
Hope this helps.
:-)