what equation do I use to solve this problem?

Question

a 350 seat movie theater charges $10.50 admission for adults and $7.50 for children. if theater is full and $3411 is collected, how many adults and how many children are in the audience?

Answer 1

You have 2 unknowns (number of adults and number of children) so you need 2 equations to solve this. Your system of equations is:

Let x be the number of adults and y the number of children

x+y=350

10.50x+7.50y=3411

 

You can use substitution or elimination to solve. I will demonstrate elimination below:

 

-7.50(x+y=350)

 

-7.50x-7.50y=-2625

10.50x+7.50y=3411

-----------------------------

3x=786

x=262  adults

Therefore y=350-262= 88 children 

Answer 2

Let A = # of adults

C = # of children

then

A + C = 350 or A = 350 - C

10.5A + 7.5C = 3411

10.5(350-C) +7.5C = 3411

3675 - 10.5C + 7.5C = 3411

-3C = -264

C = 88

then from A = 350 -C = 262