Question

John has four more quarters than dimes. If he has $5.20 in quarters and dimes, how many of each type coin does he have?

Answer 1

16 quarters and 12 dimes

Explanation:

Let 'q' be the number of quarter and 'd' be the number of dimes.

So he has,

`0.25q+0.10d= 5.20` ......................... (i)

It is given that John has 4 more quarters than dimes, so we have,

`q = d+4` ............................. (ii)

Putting the value of 'q' in equatioi (i), we get,

`0.25(d+4)+0.10d=5.20`

`0.25d+1+0.10d=5.20`

`0.35d=5.20-1`

`0.35d=4.20`

`d=12`

Putting d = 12 in the equation (ii), we get,

`q = 12+4 =16`

Therefore, John has 16 quarters and 12 dimes.

You can also verify the sum by multiplying 16 quarters with its value and adding the value of 12 dimes, you will get $5.20.

Answer 2

John has 16 quarters and 12 dimes

Explanation:

Quarters are worth $0.25 each and Dimes are worth $0.10 each.

Let number of dimes John has be
`d` and number of quarters he has be
`q`

• Given in the problem, "John has four more quarters than dimes". This means:

`q-4=d`

This is Equation 1.

• Given in the problem, "If he has $5.20 in quarters and dimes". This means:

`0.25q+0.1d=5.20`

This is Equation 2.

Now, substituting Equation 1 into Equation 2 and solving for q gives us:

`0.25q+0.1(q-4)=5.20\\0.25q+0.1q-0.4=5.20\\0.35q=5.20+0.4\\0.35q=5.60\\q=16`

There are 16 quarters.

Now using this fact, we use this value in Equation 1 to get the number of dimes.

`q-4=d\\16-4=d\\12=d`

There are 12 dimes.

Hence, John has 16 quarters and 12 dimes.