Question

Marcy has total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have?

Answer 1

Marcy has `27` quarters.

Explanation:

Write a systems of equations.

Let `x` be the number of quarters, and `y` be the number of dimes.

`x + y = 100`

`0.25x + 0.10y = 14.05`

Solve by substitution:

`y = 100 - x`

`:.`0.25x + 0.10(100 - x) = 14.05#

`0.25x + 10 - 0.10x = 14.05`

`0.15x + 10 = 14.05`

`0.15x = 4.05`

`x = 27`

Solve for `y` now:

`y + 27 =100`

`y = 100 - 27`

`y = 73`

Hence, Marcy has `27` quarters and `73` dimes.

Hopefully this helps!

Answer 2

If she had only dimes she'd have `$10.00`

Explanation:

Every time she substitutes one dime for a quarter, she adds `$0.15` to the total value. She has to add `$14.05-$10.00=$4.05`
So she will have to substitute `($4.05)/($0.15)=27` coins.

Answer: she has 27 quarters.