BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:45 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 was $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: GMATPrep

Given that on Wednesday evening, 1/3 of the tickets sold were at $1.80 per seat, the no. of $1.80 per seat = 1/3 of 600 = 200;

Thus, the total no. of $1.20 and $2.40 per seat = 600 – 200 = 400

Say the no. of $1.20 per sets were x; thus, the no. of $2.40 per seats were (400 – x).

Given that the total receipts from the sale of 600 tickets was $1,020, we have

200*1.80 + x*1.20 + (400 – x)*2.40 = 1,020

x = 250 => (400 – x) = 150.

Correct answer: A

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:45 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 was $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: GMATPrep

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

BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:45 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 was $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

Solution:

We see that the revenue generated by the $1.80 seats is 1/3 x 600 x 1.8 = 200 x 1.8 = $360. Therefore, the remaining 400 seats generate a revenue of 1,020 - 360 = $660. Now, if we let m = the number of $1.20 seats sold and n = the number of $2.40 seats sold, we can create the equation:

m + n = 400

and

1.2m + 2.4n = 660

We see that we need to solve for n. Since m = 400 - n, we have:

1.2(400 - n) + 2.4n = 660

480 - 1.2n + 2.4n = 660

1.2n = 180

n = 150

Answer: A