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nlexa
1 month ago
11

For the 7:30 show time, 140 movie tickets were sold. Receipts from the $13 adult tickets and the $10 senior tickets totaled $1,6

64. How many adult tickets and how many senior tickets were sold?
?= adult tickets ?= senior tickets
Mathematics
2 answers:
Zina [12.3K]1 month ago
8 0

Let’s denote adult tickets as x and senior tickets as y.

We can derive two equations

x + y = 140

13x + 10y = 1664

To solve this system of equations, we will apply the Gaussian elimination method (progressive elimination of variables)

By multiplying the first equation by (-10), we get

-10x-10y=-1400. Then, by adding this to the second equation, we yield

3x=264 => x=264/3=88 => x=88

Next, we will substitute x back into the initial equation before multiplication to find

88 + y = 140 => y = 140 - 88 = 52 => y = 52

So, the number of adult tickets is x=88 and the number of senior tickets is y=52

Best of luck!!!

Svet_ta [12.7K]1 month ago
7 0

Response:

88 adult tickets and 52 senior tickets

Detailed explanation:

Formulate the equation by adding the total values of each ticket category.

13a+10(140−a)=1,664

By solving this equation for a, we determine the quantity of adult tickets sold.

13a+10(140−a)=1,664

13a−10a+1,400=1,664

3a=1,664

3a=264

Thus a=88

Consequently, with 140 tickets sold, the number of senior tickets is 140−88=52.

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