an adult ticket to a school play cost $5 and a student ticket cost $3. A total of $460 was collected from the sale of 120 tickets. How many student tickets are purchased? Solve using graphing method

Answer 1

The graphing method uses both x and y coordiantes to solve a problem.

Assign x = number of adult tickets sold and y = number of student tickets sold

 

Based on the costs for each tickets (adults $5 and students $3) and the total money collect $460, we can set up an equation:

 

5x+3y= 460

Using the total number of tickets sold (120) we can set up the equation:

x+y = 120

Now we will use the two equations to solve for one of the variables.

If we multiply the second equation by 3, we will be able to isolate the x variable by subtracting the two first equations from each other.

Multiplying second equation by 3:

3* (x+y) = 120 * 3

3x + 3y = 360

 

Subtracting this equation from our first equation: 

5x+3y=460

-(3x+3y=360)

Yields:

2x = 100

Now dividing by 2:

x=50

Now use this to solve the second equation:

x+y = 120

With x=50:

50 + y = 120

Subtract 50 from each side:

y = 70

There we have that the number of student tickets sold (y) is 70.