# Help with work problem/formula

• Feb 3rd 2011, 08:02 AM
kamakookie
Help with work problem/formula
I am stuck on a word problem and can't figure out what formula to use. I know to use x for one price and y for another, but after that I'm hitting a wall.

There were 383 tickets sold to a basketball game. The ticket price for event card holders is \$1.75 and \$2.25 for non-card holders. The total amount collected was \$806.25. How many tickets were sold at each price?
• Feb 3rd 2011, 08:19 AM
Quacky
Event card holders = x
Non-Card holders = y

$x + y = 383$ (as 383 were sold in total)

$1.75x + 2.25y = 806.25$ (as the price for x was \$1.75 and y was \$2.25, and \$806.25 was the total raised)

Can you take it from here? Rearrange to get in terms of x or y, then Substitute or eliminate as you see fit.
• Feb 3rd 2011, 08:35 AM
kamakookie
I actually got that far, but I can't seem to get the same answer as the book. I know the answer is 111 tix at 1.75 and 272 at 2.25 but I don't see how they are getting it. Do I need to multiply by 100 to get rid of the decimals? My answers are way off.
• Feb 3rd 2011, 08:46 AM
e^(i*pi)
From eq1: $y = 383-x$

Sub into eq2: $1.75x+2.25(383-x) = 806.25$. Once x is known use either equation to find y.

I get the book's answer of 111 and 272
• Feb 3rd 2011, 08:48 AM
kamakookie
Thanks! I knew I'd feel stupid once I seen the answer. I can't believe I didn't catch that.