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The diagram below shows 5 identical bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of 5 bowls is 5 inches.



Part A: Write an equation using x and y to find the height of a stack of bowls based on any number of bowls.



Part B: Describe what the x and y variable represent.



Part C: Use the equation from Part A to find the number of bowls if the height of the stacked bowls is 12.5 inches.

Verified Answer :

rabanyson5

(Bowls, Height) (1, 2)  (5,5)

Slope is (5-2)/(5-1) = 3/4 inch
y = (3/4)x + b
(2) = (3/4)(1) + b
(2)-(3/4) = b

B=1.25.  Y= 0.75*x + 1.25. 

Part B
X is the number of bowls in the stack and Y is the corresponding height of the stack.

 

fichoh

The relationship between the height, y and number of bowls, x in the scenario given can be expressed thus :

  • y = 0.75x + 1.25
  • y = height of bowl ; x = number of bowls
  • 15 bowls

We could write an equation in the form ;

y = 2 + 4x

5 = 2 + 4x

4x = 5 - 2

4x = 3

x = 3/4 = 0.75

The height of the bowl rim = 0.75

The height of the base = 2 - 0.75 = 1.25

The equation for the height of bowl, y based on the number of bowls, x can be expressed thus :

  • y = 0.75x + 1.25

C.) value of x ; given a height y = 12.5 inches :

y = 0.75x + 1.25

12.5 = 0.75x + 1.25

0.75x = 12.5 - 1.25

0.75x = 11.25

Divide both sides by 0.75 to isolate x

x = 11.25 ÷ 0.75

x = 15

Therefore, the Number of bowls is 15

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