Question

Chris has a collection of dimes and quarters worth $4.25. If she has 22 coins total, how many quarters does she have?

Answer 1

Given:

Chris has a collection of dimes and quarters worth $4.25.

To number of coins = 22

To find:

The number of quarters.

Solution:

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

Total coins :
`x+y=22` ...(i)

we know that, 1 dime = $0.10 and 1 quarter = $0.25.

Total value :
`0.10x+0.25y=4.25` ...(ii)

Multiply equation (i) by 0.10 and subtract the result form (ii).

`0.10x+0.25y-0.10(x+y)=4.25-0.10(22)`

`0.10x+0.25y-0.10x-0.10y=4.25-2.20`

`0.15y=2.05`

Divide both sides by 0.15.

`y=(2.05)/(0.15)`

`y=13.6667`

Number of quarter cannot be a decimal value.

`y\approx 17`

Therefore, the number of quarter is about 17.