Question

A small fair charges an admission fee for children and adults. The cost for admission is $3 per adult and $2 per child. On a certain day, total sales were $900, and 350 people attended the fair. How many children attended the fair that day?

Answer 1

Answer:

150

Step-by-step explanation:

I will call the number of adults that attended x, and the number of children that attended y.

if the total sales were $900, and the admission fee for adults is $3 and for children is $2:

$3x+2y=900$

i will call this equation 1.

then if 350 people attended:

$x+y=350$

i will call this equation 2.

multiplying equation 2 by -3

$-3(x+y=350 )=-3x-3y=-1050$

and adding this result to equation 1:

  $3x+2y=900$   +

$-3x-3y=-1050$

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

$0x-y=-150\\y=150$

where $y$ is the amount of childen that attended the fair.

Answer 2

2c+3d=900
C=x
D=350-x
2x+3 (350-x)=900
Solve for x to get number of children
attended the fair that day
2x+1050-3x=900
2x-3x=900-1050
-1 x=-150
x=150 children

350-150=200 adult