Posted by shansen1@pacbell.net (67.119.36.206) on October 12, 2003 at 20:10:16:
In Reply to: word problem, quarters, half dollars posted by on October 12, 2003 at 17:31:35:
We have a couple of unknown things to solve, so lets start by assigning variables:
Let Q = number of quarters
Let H = number of half dollars
Since we have two unknown variables Q and H, we're going to need two independent equations to solve these variables.
The total amount of the coins is $26, so we can write down an equation which equates this dollar amount with the dollar amount of Q quarters and H half dollars. This will be our first equation:
26 = Q/4 + H/2
We also know the total number of coins is 65, and that the coins comprise only the Q quarters and H half dollars, therefore:
65 = Q + H
We now have two equations in two unknowns which can be solved in a variety of ways. Before I get too tangled up in the solution, I notice right off the bat that if I multiply the first equation by 2 and then subtract it from the second equation, the H variable will disappear, leaving only Q. Here goes:
EQN 2: 65 = Q + H
minus
EQN 1: 52 = Q/2 + H
leaves
13 = Q/2
solve this for Q (e.g., by multiplying both sides by 2)
Q = 26. This is the number of quarters.
The dollar amount of these quarters is 26/4 = $6.50
Now substitute the number of quarters, Q back into equation 2:
65 = 26 + H
Solve:
H = 39
The dollar amount of halves is 39/2 = $19.50
These two dollar amounts should add up to $26, which they do, so we are done.