A coach is comparing the cost of buying new jerseys from two different vendors. Vendor A charges $30 delivery fee plus $10 per jersey. Vendor B charges $40 delivery fee plus $8 per jersey. What is the fewest number of jerseys the coach needs to buy for Vendor B to be cheaper than Vendor A?

Question

Question 15 options:

More than 15 jerseys

More than 3 jerseys

More than 5 jerseys

More than 1 jersey

Answer 1

To find the fewest number of jerseys for which Vendor B is cheaper than Vendor A, we can set up the total cost for each vendor as follows:

• Vendor A: Total cost = Delivery fee + Cost per jersey × Number of jerseys \[ C_A = 30 + 10x \] where \(x\) is the number of jerseys.

• Vendor B: Total cost = Delivery fee + Cost per jersey × Number of jerseys \[ C_B = 40 + 8x \]

We want to find the smallest integer \(x\) such that: \[ C_B < C_A \]

Substituting the equations, we get: \[ 40 + 8x < 30 + 10x \]

Now, let's simplify this inequality:

1. Subtract \(8x\) from both sides: \[ 40 < 30 + 2x \]
2. Subtract 30 from both sides: \[ 10 < 2x \]
3. Divide by 2: \[ 5 < x \]

This means that \(x\) must be greater than 5. Therefore, the fewest number of jerseys needed for Vendor B to be cheaper than Vendor A is more than 5 jerseys.

Thus, the correct choice is:

More than 5 jerseys.