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?
- bluebellbkkLv 710 months ago
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.
- 11 months ago
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
- Anonymous11 months ago
Yes I am going to be the first
- CogitoLv 711 months ago
You'd get better answers if you put this in the "Homework Help" or "Mathematics" sections.
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- 11 months ago
Hmm let’s see . Ask your teacher
- Barkley HoundLv 711 months ago
Just create equations with 3 variables using the stated facts.
X = main floor
Y = balcony
Z = mezzanine
56X + 31Y + 30Z = 75145