Question

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.

Answer 1

Equation for the 1st company is y = 10.5x

AND Equation for the second company is  y = 7.5x + 30

Where

x = number of T shirts

y = total cost

For the total cost to be equal for both companies, we have

10.5x = 7.5x + 30

10.5 x - 7.5 x = 30

  3 x = 30

    x = 30/3

    x = 10

The Volleyball team will have to buy 10 T-shirts from each company so that their cost becomes equal.

The total amount for each company  = 10.5x = 10.5 (10) = $ 105

OR

The total amount for each company  = 7.5x + 30 = 7.5(10) + 30 = 75 + 30

                                                             = $105

Answer 2

Total 10 T-shirts to be purchased.

Total amount of T-shirts is $105.

Given:

• 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.
• $y = 10.5x, \: y = 7.5x + 30$

To find:

• 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.

Solution:

Tip: Equate the cost function

Step 1:

Calculate the total number of T-shirts.

According to the question,

'x' : number of T-shirts

'y': total cost of T-shirts

Cost of T-shirts from both companies should be same, so equate the cost function.

$\bf 10.5x = 7.5x + 30$

Take term with x to LHS

$10.5x - 7.5x = 30$

$3x = 30$

$\bf x = 10$

Thus,

Total 10 T-shirts to be purchased .

Step 2:

Calculate the cost of T-shirts.

Put the value of x in cost function.

$y = 10.5x$

$y = 10.5 \times 10$

$\bf y = \ \: 105$

Thus,

Total amount of T-shirts is $105.

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