An athletic club had \( \$ 14,200 \) to spend on equipment. It purchased 5 bikes and 3 kayaks. The kayaks were \( \$ 200 \) more than twice the price of the bikes. There is \( \$ 400 \) left over. How much money did each kayak cost?

Let's denote the price of each bike as \( b \) and the price of each kayak as \( k \). From the problem, we have the following equations: 1. The total expenditure on equipment can be expressed as: \[ 5b + 3k = 14,200 - 400 = 13,800 \] 2. We also know that the kayaks cost \( \$ 200 \) more than twice the price of the bikes: \[ k = 2b + 200 \] Now, we can substitute the second equation into the first: \[ 5b + 3(2b + 200) = 13,800 \] This simplifies to: \[ 5b + 6b + 600 = 13,800 \] \[ 11b + 600 = 13,800 \] \[ 11b = 13,800 - 600 \] \[ 11b = 13,200 \] \[ b = \frac{13,200}{11} = 1,200 \] Now that we have the price of each bike, we can find the price of each kayak. Substituting \( b = 1,200 \) back into the equation for \( k \): \[ k = 2(1,200) + 200 = 2,400 + 200 = 2,600 \] Therefore, the cost of each kayak is \( \$2,600 \).