Question

3. Students performed in a play on a Friday and a Saturday. For both performances,adult tickets cost a dollars each and student tickets cost s dollars each.On Friday, they sold 125 adult tickets and 65 student tickets, and collected $1,200. OnSaturday, they sold 140 adult tickets and 50 student tickets, and collect $1,230.125a + 65 = 1,200140a + 50s = 1,230This situation is represented by this system of equations:a. What could the equation 265a + 115s = 2,430 mean in this situation?b. The solution to the original system is the pair a = 7 and s = 5. Explain why itmakes sense that this pair of values is also the solution to the equation265a + 115s = 2,430.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

students play:

125a + 65s = 1,200 ===> Friday

140a + 50s = 1,230 ===> Saturday

Step 02:

system of equations:

a.

a = adult tickets

s = students tickets

265a + 115s = 2,430

On this day, they sold 265 adults tickets and 115 students tickets, and collect $2,430.

b.

original solution:

a = 7

s = 5

265(7) + 115(5)= 2,430

1855 + 575 = 2430

2430 = 2430

It is verified that the original solution is also valid for this equation.

That is the full solution.