Final answer:
To find after how many pairs of soccer shoes both vendors cost the same, set up two linear equations for each vendor's total cost based on the number of pairs and solve for the intersection.
Step-by-step explanation:
To find out after how many total pairs each vendor costs about the same, we need to set up two equations representing the total cost from each vendor and find their intersection point.
For Sports Shoe Warehouse, the initial cost for 11 pairs of soccer shoes is $1100, and the cost for each additional pair is $66. So, the equation representing the total cost (C1) as a function of the number of additional pairs (x), which is x > 0
is:
C1 = 1100 + 66x
For Winning Team Shoes, the initial cost for 11 pairs is $825, and each additional pair costs an additional 6% of $825. Hence, the additional cost for one pair is 0.06 * 825 = $49.50. The equation for the total cost (C2) from Winning Team Shoes is therefore:
C2 = 825 + 49.50x
To determine after how many pairs the costs are the same, we can set these equations equal to each other and solve for x:
1100 + 66x = 825 + 49.50x
Solving the equation will give us the value of x for which both vendors charge the same amount for the total number of soccer shoes.