brennan, a farmer, orders a large box of ladybugs to control pests in his greenhouse. to make sure that he…

brennan, a farmer, orders a large box of ladybugs to control pests in his greenhouse. to make sure that he was shipped as many ladybugs as he ordered, he decides to figure out approximately how many ladybugs there are in the box. he catches 30 ladybugs, marks them with special paint, and returns them to the box. then a little while later, he catches 390 ladybugs and counts 13 marked ladybugs among them. to the nearest whole number, what is the best estimate for the ladybug population?

brennan, a farmer, orders a large box of ladybugs to control pests in his greenhouse. to make sure that he was shipped as many ladybugs as he ordered, he decides to figure out approximately how many ladybugs there are in the box. he catches 30 ladybugs, marks them with special paint, and returns them to the box. then a little while later, he catches 390 ladybugs and counts 13 marked ladybugs among them. to the nearest whole number, what is the best estimate for the ladybug population?

Answer

Explanation:

Step1: Set up proportion

Let $x$ be the total lady - bug population. The proportion is $\frac{\text{marked in first catch}}{\text{total population}}=\frac{\text{marked in second catch}}{\text{size of second catch}}$, so $\frac{30}{x}=\frac{13}{390}$.

Step2: Cross - multiply

Cross - multiplying gives $13x = 30\times390$.

Step3: Solve for $x$

First, calculate $30\times390 = 11700$. Then $x=\frac{11700}{13}=900$.

Answer:

900