Bunuel wrote:
A charity sells 140 benefit tickets for a total of 2001. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?
(A) 782
(B) 986
(C) 1158
(D) 1219
(E) 1449
Let x = # of tickets sold for FULL PRICE
So, 140-x = # of tickets sold for HALF PRICE (since 140 tickets were sold in total)
Let y = the FULL PRICE cost
So, y/2 = the HALF PRICE cost
A charity sells 140 benefit tickets for a total of $2001We can write: (amount raised by FULL-price tickets) + (amount raised by HALF-price tickets) = $2001
Substitute values to get: xy + (y/2)(140 - x) = $2001
Expand to get: xy + 70y - xy/2 = $2001
Multiply both sides by 2 to get: 2xy + 140y - xy = $4002
Simplify to get:
xy + 140y = $4002How much money is raised by the full-price tickets?IMPORTANT: xy = the money is raised by the full-price tickets.
So our goal is to find the value of xyWe already know that
xy + 140y = $4002Subtract 140y from both sides to get:
xy = $4002 - 140ySince we're told the price of a full-price ticket is an INTEGER value (i.e., "a whole dollar amount"), we know that
the units digit of 140y is 0So,
xy = $4002 - (some number with units digit 0)So,
xy must have units digit 2Check the answer choices ... only answer choice A has units digit 2
Answer: A
Cheers,
Brent
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