Answer:
Number of adult tickets = 3 tickets
Number of children tickets = 5 tickets
Explanation:
A- The system of equations:
Assume that the number of adult tickets is x and that the number of children tickets is y
We are given that:
i. The total number of people in the group is 8, which means that the total number of tickets bought is 8. This means that:
x + y = 8 ..................> equation I
ii. The price of an adult ticket is $12 and that of a child ticket is $10. We know that the group spent a total of $86. This means that:
12x + 10y = 86 ...............> equation II
From the above, the systems of equation is:
x + y = 8
12x + 10y = 86
B- Solving the system using elimination method:
Start by multiplying equation I by -10
This gives us:
-10x - 10y = -80 .................> equation III
Now, taking a look at equations II and III, we can note that coefficients of the y have equal values and different signs.
Therefore, we will add equations II and III to eliminate the y
12x + 10y = 86
+( -10x - 10y = -80)
Adding the two equations, we get:
2x = 6
x = 3
Finally, substitute with x in equation I to get the value of y:
x + y = 8
3 + y = 8
y = 8 - 3 = 5
Based on the above:
Number of adult tickets = x = 3 tickets
Number of children tickets = y = 5 tickets
C- Explanation of the meaning of the solution:
The above solution means that for a group of 8 people to be able to spend $86 in a theater having the price of $12 for an adult ticket and $10 for a child' one, this group must be composed of 3 adults and 5 children
Hope this helps :)