Question

Brandon has a cup of quarters and dimes with a total value of $3.80 . The number of quarters is 4 less than twice the number of dimes. How many quarters and how many dimes does Brandon have

Answer 1

You have 15 quarters

Answer 2

Answer: The required number of quarters is 12 and that of dimes is 8.

Step-by-step explanation: Given that Brandon has a cup of quarters and dimes with a total value of $3.80 . The number of quarters is 4 less than twice the number of dimes.

We are to find the number of quarters and dimes that Brandon has.

We know that

1 quarter = 0.25 dollar and 1 dime = 0.10 dollar.

Let q and d represents the number of quarters and dimes respectively that Brandon has.

According to the given information, we have

`0.25q+0.10d=3.80\\\\\Rightarrow 25q+10d=380\\\\\Rightarrow 5q+2d=76~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and

`q=2d-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Substituting the value of q from equation (ii) in equation (i), we get

`5(2d-4)+2d=76\\\\\Rightarrow 10d-20+2d=76\\\\\Rightarrow 12d=96\\\\\Rightarrow d=(96)/(12)\\\\\Rightarrow d=8.`

And, from equation (ii), we get

`q=2*8-4=16-4=12.`

Thus, the required number of quarters is 12 and that of dimes is 8.