Question

A high school play has sold tickets to their performance and wanted to see how many tickets were adults (x) and how many were students (y). There were 50 more adult tickets sold than student tickets. Adult tickets were $5, student tickets were $2, and they collected a total of $950. What are the two equations?

Answer 1

Explanation:

Write equations as you read the problem

x - y = 50 (1)

5x + 2y = 950 (2)

First equation comes from counting persons.

Second equation comes from counting money.

There are several different methods to solve.

For example, using the Elimination method, multiply first equation by 2 (all the terms in both sides);

keep equation (1) as is.

2x - 2y = 100 (3)

5x + 2y = 950 (4)

Now add the equations. The terms "-2y" and "2y" will cancel each other, and you will get

a single equation in only one unknown x

2x + 5x = 100 + 950,

or

7x = 1050,

x = 1050/7 = 150.

Then from equation (1), y = x - 50 = 150 - 50 = 100.

ANSWER. 150 adults and 100 students.

CHECK. 5*150 + 2*100 = 750 + 200 = 950 dollars (t0tal money). ! Correct !