I don't understand how to figure this out. Couldn't you have multiple answers?
The total receipts for a basketball game are $1,400 for 788 tickets. Adults paid $2.50 and students paid $1.25. The tickets takers count only the amount of tickets, not the type of tickets sold. Determine the number of each type of ticket sold.
let the number of adult tickets sold be x
then the number of student tickets is 788-x
2.5x + 1.25(788-x) = 1400
solve for x
To solve this problem, we can use a system of equations. Let's define two variables:
Let's say x represents the number of adult tickets sold.
Let's say y represents the number of student tickets sold.
Since we know the total number of tickets sold is 788, we can write the first equation:
x + y = 788 ---(Equation 1)
We also know the total receipts from selling these tickets is $1,400. To determine the total revenue for each type of ticket, we can multiply the number of tickets sold by their respective prices:
Revenues from adult tickets: x * $2.50 = 2.5x
Revenues from student tickets: y * $1.25 = 1.25y
The total revenue can be calculated by adding these two amounts:
2.5x + 1.25y = $1,400 ---(Equation 2)
Now we have a system of equations:
x + y = 788 ---(Equation 1)
2.5x + 1.25y = $1,400 ---(Equation 2)
We can use these equations to find the values of x and y. There will be a unique solution for x and y, so we won't have multiple answers.
To solve this system of equations, we can use different methods such as substitution, elimination, or graphing. Let's use the substitution method here:
From Equation 1, we can rewrite it as x = 788 - y. We will substitute this expression for x in Equation 2:
2.5(788 - y) + 1.25y = $1,400
Now we can solve for y:
1970 - 2.5y + 1.25y = $1,400
1970 - 1.25y = $1,400
-1.25y = $1,400 - $1,970
-1.25y = -$570
y = -$570 / -1.25
y = 456
Now that we have the value of y, we can substitute it back into any of the original equations to solve for x. Let's use Equation 1:
x + 456 = 788
x = 788 - 456
x = 332
Therefore, the number of adult tickets sold (x) is 332, and the number of student tickets sold (y) is 456.