Joe has 4 less than twice as many quarters as half dollars. He has 2 less dimes than quarters. Find how many of each type of coins he has if the value of coins total $10.40.
The key to answering the many questions of this type is to learn how to translate English into mathematical language. You need to become bilingual.
Also, remember to define your terms. Follow what I've written carefully to understand each part. This is the only way that you will learn to do these problems all by yourself, which is the goal.
Q: # of quarters
H: # of half-dollars
D: # of dimes
Joe has 4 less than twice as many quarters as half dollars.
Q = 2H – 4
He has 2 less dimes than quarters.
D = Q – 2
The value of coins total $10.40.
10.40 = 0.50H + 0.25Q + 0.10D
We have three equations in three unknowns (H, Q, and D), so, with any luck, we should be able to figure out this problem.
Q is both of the first two equations, so we will express H and D in terms of Q.
Q = 2H – 4
Q + 4 = 2H – 4 + 4
Q + 4 = 2H
(Q + 4)/2 = H
D = Q – 2 <already OK>
Now we will substitute the equivalent values of D and H for D and H to get one equation with one unknown, which should be solvable.
10.40 = 0.50H + 0.25Q + 0.10D
10.40 = 0.50[(Q + 4)/2] + 0.25Q + 0.10(Q – 2)
