**1. The problem statement, all variables and given/known data**

Assume that x is a positive multiple of 5 and is greater than 5. If 2x + 1 < 100, how many values for x are possible?

**2. Relevant equations**

**3. The attempt at a solution**

How I solved the problem

First manipulated inequality:

2x+1<100

=>

2x < 99

=>

x < 49.5

Now, x is a multiple of 5 => x = 5k for some integer k > 1 (because we are given that x > 5)

x < 49.5 => 5k < 49.5 => k < 9.9

So the possible values of k (since k is an integer > 1):

2, 3, 4, 5, 6, 7, 8, 9

So there are 6 values, namely: 5(2), 5(3), 5(4), 5(6), 5(7), 5(8), 5(9) - 10, 15, 20, 25, 30, 35, 40, 45

Solution they have given:

Solution they have given:

The correct answer is 17. (To gain credit for answering the question correctly you must type the number 17 in the numeric-entry box.) Given that 2x is a multiple of 5, x must be a multiple of 2.5. The total number of such multiples from 2.5 to 50 is 20. Given that x is greater than 5 and that 2x + 1 < 100, you must eliminate 2.5, 5.0, and 50 from the list of 20 multiples, which leaves 17 possible values for x.

I am very confused by the solution they have given and have no idea what aspect of this problem I am interpreting incorrectly