Tickets to a movie cost $7.25 for adults and $5.50 for a student. A group of 8 friends purchased 8 tickets for a total of $52.75. How many adult tickets and student tickets were purchased.

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absor201 absor201 · Answer 1 · 2019-12-13T16:16:58+01:00

There were 5 adult tickets and 3 student tickets

Step-by-step explanation:

Let x be the number of adult tickets

and

y be the number of student tickets

Then according to given statements

[tex]x+y = 8\ \ \ Eqn\ 1\\7.25x+5.50y = 52.75\ \ \ Eqn\ 2[/tex]

From Eqn 1:

x = 8-y

Putting in equation 2

[tex]7.25(8-y)+5.50y = 52.75\\58 - 7.25y +5.50y = 52.75\\58 - 1.75y = 52.75\\-1.75y = 52.75-58\\-1.75y = -5.25[/tex]

Dividing both sides by -1.75

[tex]\frac{-1.75y}{-1.75} = \frac{-5.25}{-1.75}\\y = 3[/tex]

Putting y = 3 in equation 1

[tex]x+y = 8\\x+ 3 = 8\\x = 8-3\\x = 5[/tex]

There were 5 adult tickets and 3 student tickets

Keywords: Linear equations, variables

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