Question

he school production of​ 'Our Town' was a big success. For opening​ night, 491 tickets were sold. Students paid ​$1.50 ​each, while​ non-students paid $3.50 each. If a total of $ 956.50 was​ collected, how many students and how many​ non-students attended
solve the system x+y = 491
2.5x+4.5y= 956.50
x= ?
y= ?

Answer 1

What did you get for your answers?

Answer 2

im not sure where to go from here

Answer 3

Solve this system of equations.

x+y = 491
2.5x+4.5y= 956.50

Answer 4

how?

Answer 5

There are a few ways. What way you want to use. Your teacher has probably showed you a few ways to solve system of equations. You have elimination substitution. The subsitution would be to solve for y in 2.5x+4.5y= 956.50, which would be

2.5x+4.5y= 956.50
2.5x+4.5y= 956.50- 2.5x
2.5x-2.5x+4.5y= 956.50- 2.5x
4.5y= 956.50- 2.5x

\[\large \frac{4.5y}{4.5} = \frac{956.50-2.5}{4.5} \]
\[\large y= \frac{956.50-2.5}{4.5} \]

\[\large y= 212.55-.55 \]

Now take Y and substitute it into the top equation x+y=491

x+(212.55-.55)=491

Now turn those decimals to whole numbers by multiplying by 100 on both sides of the equation

100(x+(212.55-.55))=491 * 100
100x+21255-55=49100

Now just solve for x from this equation 100x+21255-55=49100. Can you solve x now?

Answer 6

yes thank you so much it makes more sense now.

Answer 7

Once you find x just put x into the equation x+y=491 and solve for y

Answer 8

okay