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

Question

2 years ago

7

. How many adult tickets and student tickets were purchased.

1 answer:

Over [174] · Answer 1 · 2023-03-22T22:37:06+03:00

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

$x+y = 8\ \ \ Eqn\ 1\\7.25x+5.50y = 52.75\ \ \ Eqn\ 2$

From Eqn 1:

x = 8-y

Putting in equation 2

$7.25(8-y)+5.50y = 52.75\\58 - 7.25y +5.50y = 52.75\\58 - 1.75y = 52.75\\-1.75y = 52.75-58\\-1.75y = -5.25$

Dividing both sides by -1.75

$\frac{-1.75y}{-1.75} = \frac{-5.25}{-1.75}\\y = 3$

Putting y = 3 in equation 1

$x+y = 8\\x+ 3 = 8\\x = 8-3\\x = 5$

There were 5 adult tickets and 3 student tickets

Keywords: Linear equations, variables

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