THERE ARE 50 DIMES
Let d be the number of dimes and n be the number of nickels. Then (because there are 75 coins), d + n = 75
Also, you can figure out the value of the money you have by multiplying the number of dimes by 0.10 and multiplying the number of nickels by 0.05. That means 0.10d + 0.05n = 6.25
This gives you 2 equations with the 2 unknowns (d and n). You can solve this in several ways, including substitution and elimination. I'll go with substitution because that's usually the first method taught.
If d + n = 75, then d = 75 - n (subtract "n" from both sides of the equation). Now since "d" is the same as "75 - n" you can plug into the second equation "75 - n" wherever you see "d". That gives you:
0.10(75 - n) + 0.05n = 6.25
7.5 - 0.10n + 0.05n = 6.25 (distributing to eliminate the parenthesis)
7.5 - 0.05n = 6.25 (combining like terms)
-0.05n = -1.25 (subtracting 7.5 from both sides)
n = 25 (dividing both sides by -0.05)
So there are 25 nickels.
Since d + n = 75, you can plug 25 in for n to get:
d + 25 = 75
d = 50 (subtracting 25 from both sides)
So there are 50 dimes