BRITTNIE B. answered • 09/09/19
Accounting and Math Tutor
To solve this problem, you can create a system of equation; for there are TWO unknown elements.
x=number of $15 dollar tickets sold
y=number of $25 dollar tickets sold
The system of equation is as follows:
x+y=8300
15x+25y= $172,500
x+y=8300 (This equation basically says that the total volume of $15 dollar tickets and $25 dollar tickets sold is 8300).
15x+25y=172,500 (This equation basically says that the dollar value of $15 dollar tickets and $25 dollar tickets sold is $172,500).
This system can be solved using various methods; however, I am going to solve by using eliminating by subtraction by eliminating the variable y.
To eliminate y by subtraction, I need the coefficient (basically the number in front of the variable) of y in both equations to be the same. Again, there is more than one approach to this. Since 25 is the coefficient of y in my second equation, I need to make 25 the coefficient of y in my first equation. I can do that by using the distributive property to multiply by first equation by 25. Please see below.
x+y=8300==> 25(x+y)=(25)(8300)=25x+25y=207,500
15x+25y= $172,500
Now, that both coefficients of y are 25, we can simply subtract to eliminate y.
10x=35,000
x=3500
Therefore, the number of $15 dollar tickets sold were 3,500 (X).
To find the number of $25 dollar tickets sold, simply substitute the value of x (which we now know is 3,500) into any of the original equations and solve for y.
x+y=8,300
3,500+y=8,300
y=4,800
We know know that the number of $25 dollar tickets sold were 4,800; and the number of $15 dollar tickets sold were 3,500.
To confirm that the answers are correct, substitute the values of each variable into EACH of the equations in your system of equations. If your answers are correct, the equations will be valid.
x+y=8300 ==> 3,500+4,800=8300 (confirmed)
15x+25y= $172,500 ==> (15)(3500)+(25)(4800)=52,500+120,000=172,500 (confirmed)
