Question

If evan has 10 dimes and quarters in his pocket, and they have combined value of 190 cents, how many of each coin does he have?

Answer 1

6 quarters and 4 dimes.

Explanation:

To solve this problem in two variables (dimes and quarters) it is necessary to write two equations.

The first equation is dimes + quarters = `10`

The second equation is `0.10` x dimes + `0.25` x quarters =$ 1.90

Now it is clear then dimes = `10` - quarters so this value can be put into the second equation giving

`0.10 xx` ( 10 - quarters) + `0.25 xx` quarters = `$ 1.90`

`$1.90 = 190` cents.

This gives

`100` cent - `10` quarters + `25` quarters = `190` cents

Now `25` quarters - `10` quarters = `15` quarters.

so `15 quarters +`100`cents =`190# cents

now subtract `100` cents from both sides

`15` quarters + `100` cents - `100` cents = `190` cents - `100` cents

giving `15` quarters = `90` cents. It takes 6 quarters

If there are `6` quarters there must be only `4` dimes

`6 + 4 = 10`

`90` cents = `0.90`

`(0.90/.15 )xx (100/100 ) = 90/15 = 6`

`6` quarters x `$0.25` /quarter = `$ 1.50`

`4` dimes x `$0.10` /dime = `$0.40`

                   Total   =        $1.90