Ms. Thayer bought 6 items for her physics class at a mean cost of $8.40 per item.

Hello GamemasterX40!  This is my attempt of solving this problem:

"Ms. Thayer bought 6 items for her physics class at a mean cost of 8.40 dollars per item. When she added a dial caliper for 46.50 dollars to her purchases, the new mean for all 7 items became about... Explain your thinking."

SOLUTION (and explanation):

We know that the mean is the average of a set of numbers. With this information in mind, we know that the total cost of the 6 items Ms Thayer bought for her class was: \[6 \times 8.40 = 50.40 \text{ dollars.}\] Now, Ms. Thayer bought a 7th item, the dial caliper, for 46.50 dollars. Adding this to our total, we get $50.40+46.50 = 96.90 \text{ dollars.}$ Again, we knot that the mean is the average of a set of numbers. That means the mean, or in the context of the problem, the average price, of the 7 objects is: \[\frac{96.90}{7}=13.8428571429... \approx 13.84 \text{ dollars.}\]

I hope this helped!