Dave has quarters, dimes and nickles in his bank. He has 3 more dimes than quarters and 6 less nickles than quarters. There are 63 total coins. How many are quarters?
I used guess and check until I got it. Sometimes you have to take the time to do this.
q 17, d 20, n 11 = 48
q 20, d 23, n 14 = 57
q 23, d 26, n 17 = 66
q 22, d 25, n 16 = 63
The last one works. 22 quarters, 25 dimes, and 16 nickels.
x Qtrs
(x + 3) dimes
(x - 6) nickles
x + (x + 3) + (x - 6) = 63
3x - 3 = 63
x = 22 Qtrs.
To solve this problem, we will set up a system of equations based on the given information:
Let's assume the number of quarters is Q.
According to the problem, Dave has 3 more dimes than quarters, so the number of dimes is Q + 3.
Also, he has 6 less nickels than quarters, so the number of nickels is Q - 6.
Now, we can write the equation based on the total number of coins. The total number of coins is the sum of the number of quarters, dimes, and nickels, which is given as 63:
Q + (Q + 3) + (Q - 6) = 63
Simplifying the equation, we get:
3Q - 3 = 63
Adding 3 to both sides of the equation, we get:
3Q = 66
Dividing both sides by 3, we get:
Q = 22
Therefore, there are 22 quarters.