A Math Word Problem

Question

if the basketball team made $1400 on tickets

they sold 788 tickets all together

the adult prices are $2.50

the student are $1.25

How many adults came??

Answer 1

Let's let x represent the NUMBER of adult tickets and y represent the NUMBER of student tickets. Since there are a total of 788 Tickets , we can write:

x + y = 788

Then since each adult ticket cost $2.50 and each student ticket cost $1.25 , we can write:

$2.50x + 1.25y = $1400

To solve these two equations with two unknowns, use substitution.

From the first equation we can write that y= 788 -x

Substitute this expression for n into the second equation:

2.50x + 1.25(788 - x) = 1400

Solve for x using inverses operations, combining like terms, and the distributive property:

2.50x + 985 - 1.25x = 1400

1.25x + 985 = 1400

1.25x + 985 - 985 = 1400 - 985

1.25x = 415

1.25x/1.25 = 415/1.25

x= 332

So the number of adult tickets is 332 . The number of student tickets will be 456 tickets OR 788 - 332

To check,332 adult tickets would cost $830 OR $2.50 * 332

456 student tickets would cost $570 OR $1.25 * 456

$830 + 570 = $1400