Question

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 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**.