Answer:
The answer to your question is he sold 47 adult tickets and 37 children tickets.
Step-by-step explanation:
Data
Adult ticket = a = $105
Children ticket = c = $60
Total number of tickets = 84
Total money earn = $7155
Equations
a + c = 84 ------------ (I)
105a + 60c = 7155 -------------(II)
Multiply equation I by -60
-60a - 60c = -5040
105a + 60c = 7155
Simplify
45a = 2115
a = 2115 / 45
a = 47 tickets
Substitute a in equation I
47 + c = 84
c = 84 - 47
c = 37 tickets
You can form linear equations from the given description then use that system to derive the solution.
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Let the amount of adult tickets sold be "a"
Let the amount of children tickets sold be "c"
Since the total amount of tickets sold is given as 84
Thus,
Total tickets = children tickets + adult tickets
84 = c + a
a + c = 84
since 1 adult ticket costs $105,
thus, "a" adult tickets cost [tex]105 \times a = 105a \text{\:\:(Written in short)}[/tex] (in dollars)
Similarly,
since 1 children ticket costs $60
"c" children tickets cost [tex]60c[/tex] (in dollars)
Since the price obtained by selling those tickets is $7155
thus,
total amount earned = amount earned by children tickets + amount earned by adult tickets
$7155 = $60c + $105a
Thus, we got the system of equations as:
[tex]a + c = 84\\105a + 60c = 7155[/tex]
Multiplying first equation with -105 to make a's coefficient equal and opposite to make the addition of them eliminate "a":
[tex]-105a -105c = -105 \times 84\\105a + 60c = 7155\\\\\text{Addding both equations}\\\\-45c = 7155 - 8820 = -1665\\\\c = \dfrac{1665}{45} = 37[/tex]
Putting this value in first equation, we get:
[tex]a + c = 84\\a + 37 = 84\\a = 84 - 37 = 47[/tex]
Thus,
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
Learn more about system of linear equations here:
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