At Willow Creek Farms, Chrissy likes to stack the mandarins in triangular pyramids. Each layer of mandarins is in the shape of an equilateral
triangle, and the top layer is a single mandarin.
1. How many mandarins are in a stack eight layers high?
2. How is this task similar to others we have done? How is it different? What types of patterns
are present in this situation?

Part (a)

Let's replace x with 15 and evaluate to see if he is correct or not.

x/2 - 3 = 6

15/2 - 3 = 6

7.5 - 3 = 6  

4.5 = 6

We get a false statement after simplifying everything. We need to get the same number on both sides to get a true statement. Therefore, Ahmed is not correct.

Part (b)

Let's solve for x. We do so by first adding 3 to both sides, and then multiplying both sides by 2. This follows PEMDAS in reverse, undoing everything to isolate the variable.

x/2 - 3 = 6

x/2 = 6+3 add 3 to both sides

x/2 = 9

x = 9*2 multiply both sides by 2

x = 18 is the answer

As a check, we'll use the same idea as part (a)

x/2 - 3 = 6

18/2 - 3 = 6

9 - 3 = 6

6 = 6

We get a true statement this time. This confirms x = 18