The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 8 cases and its height are shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 14 cases.

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The question is not complete.

The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 6 cases and its height are shown.

The height of 6 DVD cases is 114 mm

a. What is the constant of proportionality in millimeters per DVD case?

b. What is the height of 13 DVD cases in millimeters?

Solution:

a) The height of the stack of DVD is proportional to the number of cases. Let y represent the height of the stack and x represent the number of cases. Since y ∝ x, therefore:

y = kx  (where k is the constant of proportionality)

When y = 114 mm, x =6, substituting:

114 = 6k

k = 114/6

k = 19

b) The equation now becomes:

y = 19x

For 13 cases, (x = 13) the height is:

y = 19(13)

y = 247 mm

For 13 cases, the height is 247 mm

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