Question

You have a total of 52 dimes and quarters. You have 10 more quarters than dimes. Which system of equations can you use to find the number x of quarters and number y of dimes you have? Use the system to determine how much money you have in quarters and dimes.

Answer 1

`x+y=52\\\\x-y=10`

$7.75 in quarters and $2.1 in dimes.

Explanation:

If we let
`x` represent the number of quarters, and let
`y` represent the number of dimes, then we have the equation

`x+y=52` this says that the total number of dimes and quarters is 52.

And since there 10 more quarters than dimes

`x=y+10`

which can be rewritten as

`x-y=10` this says that you have 10 more quarters than dimes.

Thus we have the system of equations

(1).
`x+y=52`

(2).
`x-y=10`

and solve this system by subtracting the second equation from the first equation to get:

`2y=42\\\\\boxed{y=21}`

we have got 21 dimes.

Now we substitute
`y` into equation (1) and solve for
`x`:

`x+21=52\\\\\boxed{x=31}`

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
`31*0.25=7.75` dollars

and in dimes
`21*0.1=2.1` dollars.