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Lesson 3: Joint Proportion — Practice Questions

  1. 1. The variable $m$ varies jointly with $n$ and $p$. Which equation represents this relationship, where $k$ is the constant of proportionality?

    • A. $m = knp$
    • B. $m = \frac{k}{np}$
    • C. $m = \frac{kn}{p}$
    • D. $m = k + n + p$
  2. 2. The variable $y$ varies jointly with $x$ and $z$. If $y = 96$ when $x = 4$ and $z = 3$, what is the constant of proportionality, $k$? The value of $k$ is ___.

  3. 3. Suppose $a$ varies jointly with $b$ and $c$. If $a = 50$ when $b = 5$ and $c = 2$, what is the value of $a$ when $b = 3$ and $c = 4$?

  4. 4. The cost $C$ of producing a batch of items varies jointly with the number of workers $W$ and the hours worked $H$. If it costs 6000 dollars for 10 workers to work 30 hours, find the cost for 15 workers to work 40 hours. The cost is ___ dollars.

  5. 5. Let $P$ vary jointly with $Q$ and $R$. If $P = 120$ when $Q = 6$ and $R = 5$, what is the value of $Q$ when $P = 80$ and $R = 2$?

  6. 6. A car travels a certain distance. If its speed is tripled and its travel time is quadrupled, the new distance covered will be ___ times the original distance.

  7. 7. A cyclist travels for a certain amount of time. If their speed is quadrupled, but their travel time is reduced to one-fourth of the original time, how does the new distance compare to the original?

    • A. It is halved.
    • B. It is doubled.
    • C. It remains the same.
    • D. It is quadrupled.
  8. 8. A train's speed is increased by a factor of 5, while its travel time is cut in half. The new distance traveled is ___ times the original distance.

  9. 9. A boat travels a certain distance. If its speed is halved and the travel time is also halved, what is the effect on the distance traveled?

    • A. The distance is one-fourth of the original.
    • B. The distance is halved.
    • C. The distance is unchanged.
    • D. The distance is doubled.
  10. 10. A plane's speed is reduced to two-thirds of its original speed, and its flight time is cut in half. The new distance is ___ of the original distance. (Enter as a fraction)