It is time to post the solution to the Body Builder, Masks and Dumbbells algebra maths puzzle that was posted last week.

If you have not had a go at solving this puzzle and registering your answer on the poll; Stop reading the solution, click on the link above and go do it now. 🙂

The puzzle image is shown below:

Here is the “initial” solution:

- There are three body builders which total 15, so each body builder is 5.
- There are three masks which total 9, so each mask is 3.
- There are three dumbbells which total 18, so each dumbbell is 6.
- The final sum is (2 x 6) + 5 x 3
- Doing multiplication first gives 12 + 15.
- So the final answer is 27 …. Which is incorrect.

Look at the image and you will notice the following:

- The body builder in the final equation is holding a dumbbell and wearing a mask (very responsible when at the gym in today’s world).

So let’s redo the final equation:

- The final sum is (2 x 6) + (5 + 6 + 3) x 3 = 12 + 14 x 3
- Doing multiplication first gives 12 + 42.
- So the final answer is 54…. Which is also incorrect.

Look at the image even closer and you will notice the following:

- The dumbbells have 3 weights per side initially, but only 2 weights per side in the final equation.

So let’s start again with a more accurate solution:

- There are three body builders which total 15, so each body builder is 5. Unchanged
- There are three masks which total 9, so each mask is 3. Unchanged
- There are three dumbbells (3 weights per side) which total 18, so each large dumbbell is 6.
- Now what is the weight of the smaller dumbbell (2 weights per side)?
This is a difficult question that requires an assumption, and as we all know to

**assume**something just makes and**ass**out of**u**and**me**. 😁If we assume that the bar itself has no weight or is included in the largest weight and we assume that each weight pair weighs 3, 2, & 1 respectively (i.e., individual weights are 1.5, 1.0 and 0.5) totalling to 6. Then if we remove the smallest weight pair, the dumbbell now weights 5. This approach could be disputed which could then change the final equation and final answers.

- The final sum is (2 x 5) + (5+5+3) x 3 = 10 + 13 x 3
- Doing multiplication first gives 10 + 39.
- So the final answer is
**49**… if the assumptions made about the smaller dumbbells are correct.

Where you observant? Did you notice the smaller dumbbells? What assumptions did you make about the weight of the smaller dumbbell? At the time of posting this article, only 15% of respondents on the poll agree this solution.

However, the most popular response (54) does not take into account the change in the dumbbells for the final equation and the second most popular response (78) does not take into account the change in the dumbbells AND does not follow the order of operations rules by doing multiplication first. So we know those two answers are incorrect.

Keep safe, well and sane.

David

This article was originally posted on http://www.winthropdc.com/blog.