Discussion
Z varies jointly as X and Y. If Z = 34 when X = 14 and Y = 51, then find the constant of proportionality.
Answer: B
The constant is 1/21.
Z varies jointly as X and Y, so Z = kXY. Substituting Z = 34, X = 14 and Y = 51 gives 34 = k × 714.
\[ k=\frac{34}{14\times51}=\frac{34}{714}=\frac{1}{21} \]
The other fractions would give a different value of Z.
The constant of proportionality is the number that multiplies X and Y to give Z. Putting the values back checks it: (1/21) × 14 × 51 = 714/21 = 34, as given. The other fractions would give 170, 68 or 272/3 rather than 34.
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