No. of adult tickets = 102
No. of children tickets = 46
Step-by-step explanation:
Given
they sold 148 tickets. They charge $10 for adults and $5 for children. They made $1,250
a) define your variables
Let a be the number of adult tickets
and
Let c be the number of children tickets
b) write a linear equation to represent the number of tickets sold.
The equation will be:
[tex]a+c = 148\ \ \ Eqn\ 1[/tex]
c) write a linear equation to represent the amount of money made from tickets
[tex]10a+5c = 1250\ \ \ Eqn\ 2[/tex]
d) solve the system of equations. how many adult tickets and how many children's tickets were sold?
From equation 1:
[tex]a = 148 - c[/tex]
Putting in equation 2:
[tex]10(148-c)+5c = 1250\\1480-10c+5c = 1250\\1480-5c = 1250\\-5c = 1250-1480\\-5c = -230[/tex]
Dividing both sides by -5
[tex]\frac{-5c}{-5} = \frac{-230}{-5}\\c = 46[/tex]
Putting c=46 in eqn 1
[tex]a+46 = 148\\a = 148-46\\a = 102[/tex]
Hence,
No. of adult tickets = 102
No. of children tickets = 46
Keywords: Linear equations, Variables
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