Final answer:
To determine the number of volleyball shoe pairs where two vendors' costs are the same, equations based on both vendors' pricing structures were simultaneously solved, yielding approximately 17 pairs as the point where both have similar costs.
Step-by-step explanation:
The student is asking about finding the number of pairs of volleyball shoes where the costs from two different vendors are the same. To solve this, we must set up an equation where the cost of shoes from both vendors is equal and then solve for the number of pairs.
The cost from Sports Shoe Warehouse for 6 pairs is $600, and for each additional pair, it costs $83. The cost from Winning Team Shoes for 6 pairs is $480, plus 11% of the initial amount for each additional pair.
The equation for Sports Shoe Warehouse is:
C = 600 + 83(x - 6)
And the equation for Winning Team Shoes is:
C = 480 + 0.11 × 480 × (x - 6)
We can solve these equations simultaneously to find out the value of 'x' (the number of pairs) where the costs equal each other:
600 + 83(x - 6) = 480 + 0.11 × 480 × (x - 6)
After solving the equation, we find that the costs are about the same when the total number of pairs is approximately 17.