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.

The height of 8 DVD cases is 120 mm.
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Part 1
The constant of proportionality is
  
enter your response here millimeters per DVD case.

1 answer

To find the constant of proportionality, we need to divide the height of the stack by the number of cases.

In this case, we have:

  • Height of the stack (for 8 cases) = 120 mm
  • Number of cases = 8

The constant of proportionality (k) can be calculated as follows:

\[ k = \frac{\text{Height}}{\text{Number of cases}} = \frac{120 \text{ mm}}{8 \text{ cases}} = 15 \text{ mm per case} \]

Now, to find the height of a stack of 14 cases using the constant of proportionality:

\[ \text{Height for 14 cases} = k \times \text{Number of cases} = 15 \text{ mm per case} \times 14 \text{ cases} = 210 \text{ mm} \]

In summary:

  • The constant of proportionality is 15 mm per DVD case.
  • The height of a stack of 14 cases is 210 mm.