SOLUTION: abe bought 72 tickets to see harry potter on broadway some tickets cost $75.00 and the others cost $85.00 he charged 5520.00 to his american express how many tickets did he buy

Question 18432: abe bought 72 tickets to see harry potter on broadway
some tickets cost $75.00 and the others cost $85.00
he charged 5520.00 to his american express
how many tickets did he buy at each price
thanks very very much
Answer by smik(40) (Show Source): You can put this solution on YOUR website!
Good problem. This problem requires for us to make two equations and solve them using elimination or substitution. First of all we know that he bought 72 tickets in total therefore, we can say: x + y = 72.

Now, we can make a second equation, because we know that the tickets cost $75 and $85, and the final cost was $5520. Therefore, 85x + 75y = 5520. Now we can just rearrange the first equation:

x+y=72 (subtract x from each side)
y=72-x

Which enables us to substitute for y in the second equation. After substituting we get:

85x+75(72-x)=5520

Now we can foil everything out to get:

85x+5400-75x=5520 (add the like terms and subtract 5400 from each side)
5x=120 (divide both sides by 5 to solve for x)
x=24

Now we know that Abe bought 24 $85 tickets. With this information we can determine how many $75 tickets Abe bought, as we can now plug 24 into the first equation.

y = 72 - (24)
y = 48

Hence we know that Abe bought 48 $75 tickets and 24 $85 tickets.
Great Question!
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