Question

A small art museum charges $5 for an adult ticket and $3 for a student

Answer 1

There were 37 student tickets and 52 adult tickets

Step-by-step explanation:

Let x be the number of student tickets and y be the adult tickets

Then

According to given statement that total 89 tickets were sold

x+y=89     Eqn 1

And

$5 for an adult ticket and $3 for student ticket ,and total cost $371

3x+5y=371    Eqn 2

From eqn 1

$x=89-y$

Putting in eqn 2

$3(89-y)+5y=371\\267-3y+5y=371\\267+2y=371$

Subtracting 267 from both sides

$267+2y-267=371-267\\2y=104$

Dividing both sides by 2

$\frac{2y}{2}=\frac{104}{2}\\y=52$

Putting y=52 in eqn 1

$x+52=89\\x=89-52\\x=37$

Hence,

There were 37 student tickets and 52 adult tickets

Keywords: Linear Equation, Variable

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