The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The two companies, Shirt Box and Just Tees, are represented by this system of equations where x is the number of T-shirts and y is the total cost of the T-shirts.
y = 10.5x
y = 7.5x + 30
How many T-shirts would the volleyball team need to purchase from each company for the total cost to be equal?
For the total cost to be the same for both companies, the volleyball team would need to purchase
T-shirts from each company for a total of $
for each company.
10.5x = 7.5x + 30
Solve for x.
To find the number of T-shirts that the volleyball team needs to purchase from each company for the total cost to be equal, we need to set the two equations equal to each other:
10.5x = 7.5x + 30
To solve for x, we can subtract 7.5x from both sides:
10.5x - 7.5x = 7.5x - 7.5x + 30
3x = 30
Dividing both sides by 3:
3x/3 = 30/3
x = 10
So, the volleyball team would need to purchase 10 T-shirts from each company for the total cost to be equal.
To find the number of T-shirts the volleyball team would need to purchase from each company for the total cost to be equal, we need to find the values of x and y that satisfy both equations.
Let's set the two equations equal to each other:
10.5x = 7.5x + 30
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 7.5x from both sides:
10.5x - 7.5x = 7.5x + 30 - 7.5x
Simplifying the equation:
3x = 30
Now we can solve for x by dividing both sides by 3:
x = 30/3
x = 10
So the volleyball team would need to purchase 10 T-shirts from each company for the total cost to be equal.
To find the total cost for each company, we can substitute the value of x into either of the original equations. Let's use the first equation:
y = 10.5x
Substituting x = 10:
y = 10.5 * 10
y = 105
Therefore, the total cost for each company would be $105.