Answer:
Let x = number of dimes
y = number of quarters
Equation 1 is then x + y = 100, that one is easy.
Now you have to worry about values of each, and since a dime is $0.10 and a quarter is $0.25, that means that the number of each times their respective dollar amounts has to add up to the total dollar amount.
Equation 2 is then 0.1x + 0.25y = 14.05
To rewrite for clarity you have:
x + y = 100 (1)
0.1x + 0.25y = 14.05 (2)
Now you can solve this any number of ways, I'm going to use addition by multiplying both sides of equation 1 by -1/10 and then adding it to equation 2.
-0.1x - 0.1y = -10
0.1x + 0.25y = 14.05
0.15y = 4.05
don't let the decimals trip you up, that's the same as
15y = 405
y = 27 quarters
Now use that value in the original equation 1 to get
x = 100 - 27 = 73 dimes
To check use the values in the equation 2
$0.1*(73) + $0.25*(27) = $14.05
$7.30 + $6.75 = $14.05
