# Help with Math HW?

The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are \$56, balcony tickets are \$31, and mezzanine tickets are \$30. One particular night, sales totaled \$75,145. There were 256 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 336 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?

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• Y!A posted your question under 'Theatre and Acting' for obvious reasons. It is the responsibility of the person asking the question to check that it has been posted in a suitable category. OBVIOUSLY this should be in 'Homework Help' or 'Mathematics'.

You are the only person who can move it, so click on EDIT and choose another category.

• This should have been asked in science/math section, but I think I can help.

First I assigned A as number of main floor seats, B as number of balcony seats, and C as number of mezzanine seats sold. We can set up several equations:

A*56 + B*31 + C*30 = 75,145;

A = B+56;

B = 3*C+336,

3*C = B-336,

C = B/3 - 112;

The idea is to reduce the first equation to a single variable, A, B or C.

Therefore, we can substitute (B+56) for A, and we can substitute (B/3-112) for C.

The first equation becomes:

(B+56)*56 + B*31 + (B/3-112)*30 = 75,145;

56B + 3136 + B31 + 10B - 3360 = 75,145 --- collecting terms;

97B - 224 = 75145;

97B = 75369;

B = 75369 / 97 = 777 (tickets sold in the balcony) ;

Use this value with the other expressions to determine other seats sold.

A = B+56 = 777+56 = 833 seats sold on the main floor;

C = B/3 - 112 = 777/3 -112 = 259 - 112 = 147 seats sold in the mezzanine.

Now we can check by putting these numbers into the first equation:

833(56)+777(31)+147(30) = \$75,145 … answers confirmed correct

• Joe2 months agoReport

how do you get A = B+56?

• Yes I am going to be the first

• You'd get better answers if you put this in the "Homework Help" or "Mathematics" sections.

• Just create equations with 3 variables using the stated facts.

X = main floor

Y = balcony

Z = mezzanine

For example

56X + 31Y + 30Z = 75145

etc