Subject: Word Problem
Name: Sabrina
Who are you: Student

Thomas bought a badminton racquet and paid for it in quarters. If Thomas had used nickels and dimes, he would have needed 20 more dimes than quarters and one more than twice as many nickels as quarters. How much much did the badminton racquet cost?

Hi Sabrina.

Try using equations to solve the problem.

Let Q be the number of quarters Thomas spent.
Let N be the number of nickels and D be the number of dimes.

Then "he would have needed 20 more dimes than quarters" is the same as writing:

Q + 20 = D

and "one more than twice as many nickels as quarters" means:

2Q + 1 = N

The question asks for the cost (let's call that C). So you also know that if he paid in quarters,

(.25)Q = C

and if he paid in the nickels and dimes,

(.10)D + (.05)N = C

Logically, if two different things equal a common third thing, they equal each other, so

.25Q = .10D + .05N

Now you can use the two earlier equations to substitute for D and N and then solve for Q. That will determine the cost of the item.

Hope this helps,
Stephen La Rocque.