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

Answer:

John has 16 quarters and 12 dimes

Step-by-step 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.

Answer 2

Answer:

16 quarters and 12 dimes

Step-by-step 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.