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Question
If n varies directly as m, complete the following table.
| m | 3 | 5 | 6.5 | ______ | 1.25 |
| n | 12 | 20 | ______ | 28 | ______ |
Solution
It is given that n varies directly as m, i.e.,
\[n \propto m\]
∴ n = km, where k is the constant of variation
When m = 3, n = 12.
∴ 12 = k × 3
k = `12/3`
⇒ k = 4
So, the equation of variation is n = 4m.
When m = 6.5,
n = 4 × 6.5
n = 26
When n = 28,
28 = 4 × m
m = `28/4`
⇒ m = 7
When m = 1.25,
n = 4 × 1.25
n = 5
The complete table is given below.
| m | 3 | 5 | 6.5 | 7 | 1.25 |
| n | 12 | 20 | 26 | 28 | 5 |
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