Question

after a shipwreck, jamie is stranded on a desert island. he needs to build a shelter, so he makes an axe using materials from the wreckage and starts cutting down trees.
there is a proportional relationship between the number of days jamie is stranded on the island, x, and the total number of trees he cuts down, y.
what is the constant of proportionality? write your answer as a whole number or decimal.
trees per day

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \(y = kx\), the constant of proportionality \(k=\frac{y}{x}\).

Step2: Calculate \(k\) using the first pair of values

Using \(x = 3\) and \(y=15\), \(k=\frac{15}{3}\).

Step3: Simplify the fraction

\(\frac{15}{3}=5\).

Step4: Verify with other pairs

For \(x = 10,y = 50\), \(\frac{50}{10}=5\); for \(x = 12,y = 60\), \(\frac{60}{12}=5\); for \(x = 16,y = 80\), \(\frac{80}{16}=5\).

Answer:

5