A movie theater sold 120 tickets to the matinee showing of a

BTGmoderatorDC wrote:A movie theater sold 120 tickets to the matinee showing of a popular children's movie, and 150 tickets to the evening showing. The theater sold the same number of adult tickets for each show, but for the evening show was just 20 children's tickets short of selling twice as many children's tickets as it did for the matinee. How many children's tickets were sold to the evening show?

A. 50
B. 60
C. 70
D. 80
E. 90

OA D

Source: Veritas Prep

Say the number of adult tickets sold for each show is x and the number of children's tickets sold for the matinee show is y; thus, the number of children's tickets sold for the evening show would be 2y – 20.

Thus, for the matinee show, we have x + y = 120; and for the evening show, we have x + (2y – 20) = 150. From both the linear equations, we get y = 50, thus, the number of children's tickets sold for the evening show = 2y – 20 = 2*50 – 20 = 80.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:A movie theater sold 120 tickets to the matinee showing of a popular children's movie, and 150 tickets to the evening showing. The theater sold the same number of adult tickets for each show, but for the evening show was just 20 children's tickets short of selling twice as many children's tickets as it did for the matinee. How many children's tickets were sold to the evening show?

A. 50
B. 60
C. 70
D. 80
E. 90

OA D

Source: Veritas Prep

The theater sold the same number of adult tickets for each show
Let A = # of adult tickets sold for MATINEE show
So, A = # of adult tickets sold for EVENING show

The evening show was just 20 children's tickets short of selling twice as many children's tickets as it did for the matinee
In other words, if they had sold 20 extra children's tickets for the evening show, then the number of children's tickets for the evening show would have been TWICE the number of children's tickets for the matinee show
So, we can write: (# of EVENING show children's tickets) + 20 = 2(# of MATINEE show children's tickets)
Another way to write this is: (# of EVENING show children's tickets) = 2(# of MATINEE show children's tickets) - 20

Let C = # of children's tickets sold for MATINEE show
So, 2C - 20 = # of children's tickets sold for EVENING show

A movie theater sold 120 tickets to the matinee showing of a popular children's movie, and 150 tickets to the evening showing
We can write the following:
A + C = 120
A + (2C - 20) = 150

Rewrite as:
A + 2C = 170
A + C = 120

Subtract bottom equation from top equation to get: C = 50
So, 50 children's tickets were sold for the MATINEE show.

How many children's tickets were sold to the evening show?
We already know that 2C - 20 = # of children's tickets sold for EVENING show
Since C = 50, we can replace C with 50 to get: 2(50) - 20 = # of children's tickets sold for EVENING show
Evaluate: 80 = # of children's tickets sold for EVENING show

Answer: D

Cheers,
Brent

BTGmoderatorDC wrote:A movie theater sold 120 tickets to the matinee showing of a popular children's movie, and 150 tickets to the evening showing. The theater sold the same number of adult tickets for each show, but for the evening show was just 20 children's tickets short of selling twice as many children's tickets as it did for the matinee. How many children's tickets were sold to the evening show?

A. 50
B. 60
C. 70
D. 80
E. 90

OA D

Source: Veritas Prep

We can let a = the number of adult tickets sold for each show, x = the number of children’s tickets sold for the evening show, and y = the number of children’s tickets sold for the matinee.

The number of children’s tickets for the evening show was just 20 tickets short of selling twice as many children's tickets as were sold for the matinee, which we can express as:

x = 2y - 20

We also have that:

a + x = 150

Substituting (2y - 20) for x, we have:

a + 2y - 20 = 150

a + 2y = 170

We also have the following equation for the matinee ticket sales:

a + y = 120

Subtracting a + y = 120 from a + 2y = 170, we have:

y = 50

So x = 2(50) - 20 = 80 children’s tickets were sold for the evening show.

Answer: D