Question

kayoko is making a garden that is 4 feet wide and 10 feet long. she digs up a 2 x 4 foot rectangle in one end of the garden and counts 48 worms. how many worms are most likely in the whole garden? a. 240 b. 180 c. 160 d. 200

Explanation:

Step1: Calculate the area of the sampled rectangle

The area of the $2\times4$ - foot rectangle is $A_{1}=2\times4 = 8$ square - feet.

Step2: Calculate the area of the whole garden

The area of the whole garden which is $4$ feet wide and $10$ feet long is $A_{2}=4\times10=40$ square - feet.

Step3: Set up a proportion

Let $x$ be the number of worms in the whole garden. We set up the proportion $\frac{48}{8}=\frac{x}{40}$ because the ratio of the number of worms to the area in the sampled rectangle should be the same as the ratio of the number of worms in the whole garden to the area of the whole garden.

Step4: Solve the proportion

Cross - multiply gives $8x = 48\times40$. Then $x=\frac{48\times40}{8}$. Since $48\times40 = 1920$ and $\frac{1920}{8}=240$.

Answer:

A. 240