At the movie theatre word problem

Question

At the movie theatre, child admission is $5.10

and adult admission is $8.20

On Saturday, 140 tickets were sold

for a total sales of $906.20

How many child tickets were sold that day?

Answer 1

Sometimes it's easier to use the substitution method, particularly when one of the equations is c + d = 140. Then d = 140 - c and can substitute for d in the other eqn. 5.10c + 8.20d = 906.20 becomes

5.10c + 8.20(140 - c) = 906.20. The distribution rule results is 5.10c + 1148 - 8.20c = 906.20.

From there on it's a question of combining like terms: - 3.1c = -241.80 and c = 78. Then d = 140 - 78 = 62, although they only required the no. of child's tickets.

Check: 78($5.10) + 62($8.20) = $906.20

Answer 2

This problem can be approached by converting the information into a system of linear equations, then solving the system. Use variables c and d indicate the number of child and adult tickets sold. Then:

"On Saturday, 140 tickets were sold" => c + d = 140 (equation #1)

"child admission is $5.10 and adult admission is $8.20...for a total sales of $906.20" => 5.1c + 8.2d = 906.2 (equation #2)

Solving this system of two equations in two variables is then done by multiplying one equation by a constant such that adding the quantities on both sides of the equations causes one variable to disappear. For instance, multiplying Equation #1 by -8.2 yields

-8.2c + -8.2d = -8.2*140 = -1148

and adding both sides of

-8.2c + -8.2d = -1148

5.1c + 8.2d = 906.2

yields

-3.1c = -1148 + 906.2

which simplified is

-3.1c = -241.8

c = 78