5 adult tickets and 3 student tickets were purchased.
Step-by-step explanation:
Given,
Cost of one adult ticket = $7.25
Cost of one student ticket = $5.50
Total tickets purchased = 8
Total amount spent = $52.75
Let,
Number of adult tickets = x
Number of student tickets = y
According to given statement;
x+y=8 Eqn 1
7.25x+5.50y=52.75 Eqn 2
Multiplying Eqn 1 by 5.50
[tex]5.50(x+y=8)\\5.50x+5.50y=44.00\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](7.25x+5.50y)-(5.50x+5.50y)=52.75-44.00\\7.25x+5.50y-5.50x-5.50y=8.75\\1.75x=8.75[/tex]
Dividing both sides by 1.75
[tex]\frac{1.75x}{1.75}=\frac{8.75}{1.75}\\x=5[/tex]
Putting x=5 in Eqn 1
[tex]5+y=8\\y=8-5\\y=3[/tex]
5 adult tickets and 3 student tickets were purchased.
Keywords: linear equation, subtraction
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