Final answer:
The student council earned a total of $1350 by selling 150 tickets.
Step-by-step explanation:
To calculate the amount of money the student council earned, we need to determine how many tickets were sold for each price.
The student council sold a total of 150 tickets. Let's assume they sold x tickets for $8 each and y tickets for $10 each.
Therefore, we have the equation x + y = 150.
Since the council sold 150 tickets in total, the amount of money earned is 8x + 10y. By substituting the value of x from the first equation into the second equation, we get 8(150 - y) + 10y.
Simplifying that expression, we get 1200 - 8y + 10y, which equals 1200 + 2y.
To find the value of y, we can substitute the equation x + y = 150 into the expression above as x = 150 - y. We then have 1200 + 2(150 - y).
By solving for y, we get 1200 + 300 - 2y, which simplifies to 1500 - 2y.
Since the student council earned $8x + $10y = 8(150 - y) + 10y = 1200 + 2y, we can substitute the equation 1500 - 2y into this expression as $8x + $10y = 1500 - 2y.
This equation allows us to solve for y. By simplifying the expression, we get 1200 + 2y = 1500 - 2y.
Combining like terms, we have 4y = 300. Dividing both sides by 4, we get y = 75.
Now that we know the value of y, we can substitute it back into the equation x + y = 150 to find x. Therefore, x = 150 - 75, which equals x = 75.
The student council sold 75 tickets for $8 each and 75 tickets for $10 each. To calculate the total earnings, we can substitute the values of x and y into the expression for money earned: 8(75) + 10(75) = 600 + 750 = $1350.
Therefore, the student council earned a total of $1350 by selling 150 tickets.