To raise money, the student council at a local middle school is hosting a talent show. Tickets are sold for $5.00 for students (x) and $8.00 for adults (y). The goal is to raise a total of $1,575.00. Which of the following is a viable solution for the number of student and adult tickets that can be sold?
• (125,115)
• (81,146.25)
• (115,125)
• (371,-35)
To determine which of the given solutions is viable, we can set up an equation based on the information given.
Let x represent the number of student tickets sold and y represent the number of adult tickets sold.
According to the problem, the total amount raised is given by the equation:
5x + 8y = 1575
We can now substitute the given solutions one by one to check if they satisfy the equation.
1. (125, 115):
Substituting x = 125 and y = 115 into the equation:
5(125) + 8(115) = 625 + 920 = 1545, which is not equal to 1575.
2. (81, 146.25):
The number of tickets should be whole numbers, so this solution is not viable.
3. (115, 125):
Substituting x = 115 and y = 125 into the equation:
5(115) + 8(125) = 575 + 1000 = 1575, which is equal to the goal.
4. (371, -35):
The number of tickets cannot be negative, so this solution is not viable.
Therefore, the viable solution for the number of student and adult tickets that can be sold is (115, 125).