Question

40 coins .25 and .10 how many to make $7.75

Answer 1

7.75
40 coins.
But you have a quarter and a dime. (.35)
so,
3 quarters, subtract .35 = 75-35=40
There's my answer.

Answer 2

D + Q = 40 so D = 40 - Q
.25Q + .10D = 7.75

substitute D = 40 - Q into .25Q + .10D = 7.75
.25Q + .10D = 7.75
.25Q + .10(40 - Q) = 7.75
.25Q + 4 - .10Q = 7.75
.15Q = 3.75
Q = 25

D = 40 - 25 = 15

answer
Quarter = 25 coins
Dime = 15 coins

double check

25 + 15 = 40 coins total
25(.25) + 15(.10) = 6.25 + 1.5 = 7.75