2. PYRAMIDS When climbing an ancient
Mayan pyramid, the Johnson family
noticed that the bottom of each side of the pyramid started with 50 large
stones. The next step up had 45 large
stones, the next step up had 40 stones, and so on. Write an equation to represent the number of stones on each level. How many levels can the pyramid
have?
Steps 1 = 45 stones
Steps 2 = 40 stones
Steps 3 = 34
?
Do you have a typo for steps 3= 34 , should it be 35?
level 0 = 50
level 1 = 45
level 2 = 40
...
level n = -5n + 50
so if level n = 0
-5n+50=0
-5n=-50
n=10
counting ground level (level 0) there would be 11 levels
yes its a typo! 35
I like how you explain it. I now understand. Thanks Reiny!
To find an equation that represents the number of stones on each level of the pyramid, we can analyze the given information. We are told that the number of stones decreases by 5 for each step up.
Let's consider the pattern in the number of stones:
Step 1: 50 stones
Step 2: 45 stones
Step 3: 40 stones
...
We can observe that the difference between each step is 5. We can represent this in an equation using arithmetic progression:
number of stones = first term + (step number - 1) * common difference
In this case, the first term is 50, the common difference is -5 (since the number of stones is decreasing by 5 for each step), and the step number represents which level of the pyramid we are on.
Thus, the equation to represent the number of stones on each level is:
number of stones = 50 + (step number - 1) * (-5)
To find the number of levels the pyramid can have, we need to determine when the number of stones becomes zero or negative. Let's solve the equation when the number of stones is equal to zero:
0 = 50 + (step number - 1) * (-5)
Simplifying the equation:
(step number - 1) * (-5) = -50
Dividing both sides by -5:
(step number - 1) = 10
Adding 1 to both sides:
step number = 11
Therefore, the pyramid can have a maximum of 11 levels.