M7MBA wrote: ↑Fri Mar 19, 2021 7:11 am
A theater with 600 seats sells tickets at $1.20, $1.80, or $2.40 per seat. On Wednesday evening, 1/3 of the tickets sold were at $1.80 per seat and the total receipts from the sale of 600 tickets were $1,020. How many of the tickets sold were at $2.40 per seat?
A. 150
B. 160
C. 200
D. 250
E. 300
Answer:
A
Source: GMAT Prep
Given: 600 tickets were sold
One third of those tickets were at $1.80 per seat
1/3 of 600 = 200
So, 200 tickets sold for $1.80 per seat
And
the remaining 400 tickets were sold for either $1.20 each of $2.40 each
Let x = the NUMBER of tickets sold for $2.40
So, 400 - x = the NUMBER of tickets sold for $1.20
The total receipts from the sale of 600 tickets was $1,020
In other words:
(receipts from the $1.20 tickets) + (receipts from the $1.80 tickets) + (receipts from the $2.40 tickets) = $1,020
(200)($1.80) = $360
So, $360 = the total receipts from the $1.80 tickets
Likewise, (400 - x)($1.20) = the total receipts from the $1.20 tickets
And (x)($2.40) = the total receipts from the $2.40 tickets
Substitute values into our "word equation" to get: (400 - x)($1.20) + $360 + (x)($2.40) = $1020
Expand to get: 480 - 1.20x + 360 + 2.40x = 1020
Simplify to get: 840 + 1.20x = 1020
Subtract 840 from both sides: 1.20x = 180
Solve: x = 180/1.20 = 150
Answer: A
Cheers,
Brent
