Answer:
[tex]x+y=52\\\\x-y=10[/tex]
$7.75 in quarters and $2.1 in dimes.
Step-by-step explanation:
If we let [tex]x[/tex] represent the number of quarters, and let [tex]y[/tex] represent the number of dimes, then we have the equation
[tex]x+y=52[/tex] this says that the total number of dimes and quarters is 52.
And since there 10 more quarters than dimes
[tex]x=y+10[/tex]
which can be rewritten as
[tex]x-y=10[/tex] this says that you have 10 more quarters than dimes.
Thus we have the system of equations
(1). [tex]x+y=52[/tex]
(2). [tex]x-y=10[/tex]
and solve this system by subtracting the second equation from the first equation to get:
[tex]2y=42\\\\\boxed{y=21}[/tex]
we have got 21 dimes.
Now we substitute [tex]y[/tex] into equation (1) and solve for [tex]x[/tex]:
[tex]x+21=52\\\\\boxed{x=31}[/tex]
we have got 31 quarters.
Since a quarter is worth $0.25 and a dime is $0.1, the amount of money we have is
in quarters [tex]31*0.25=7.75[/tex] dollars
and in dimes [tex]21*0.1=2.1[/tex] dollars.
