Question

On a consert the tickets cost 3$ for children, and 5$ for adults. The combined income is 360$ and 84 tickets were sold. How many children and how many adults bought tickets?

Answer 1

Let x equal the # of child tickets

Let y equal the # of adult tickets

x + y = 84

3x + 5y = 360

Solve and state the answer. Use the substitution method to solve this system. Solve the first equation for x.

x + y = 84

x = 84 - y

Now substitute the resulting expression into the other equation and solve for y.

3( 84 - y ) + 5y = 360

252 - 3y + 5y = 360

Combine like terms

252 + 2y = 360

Subtract 252 from both sides

2y = 108

Divide by 2 on both sides

y = 54

Substitute the value of y into the equation that we solved for​ x, x = 84 - y

x = 84 - 54

x = 30

Therefore the answer should be, 30 childrens tickets sold and 54 adult tickets sold.