Question

a trog catches insects for their lunch. the trog likes to eat flies and mosquitoes in a certain ratio, which the diagram shows.
flies
diagram of 3 rectangles for flies, 7 rectangles for mosquitoes
mosquitoes
the table shows the number of flies and the number of mosquitoes that the frog eats for two lunches.
based on the ratio, complete the missing values in the table.
day | flies | mosquitoes
monday | 15 | blank
tomorrow | blank | 14

Explanation:

Step1: Determine the ratio of flies to mosquitoes

From the diagram, the number of fly - rectangles is 3 and the number of mosquito - rectangles is 7. So the ratio of flies to mosquitoes is \(3:7\).

Step2: Calculate the number of mosquitoes on Monday

Let the number of mosquitoes on Monday be \(x\). We know that the ratio of flies to mosquitoes is \(3:7\), and the number of flies on Monday is 15. So we set up the proportion \(\frac{3}{7}=\frac{15}{x}\). Cross - multiplying gives us \(3x = 15\times7\), which simplifies to \(3x=105\). Then, dividing both sides by 3, we get \(x=\frac{105}{3}=35\).

Step3: Calculate the number of flies on Tuesday

Let the number of flies on Tuesday be \(y\). The ratio of flies to mosquitoes is still \(3:7\), and the number of mosquitoes on Tuesday is 14. So we set up the proportion \(\frac{3}{7}=\frac{y}{14}\). Cross - multiplying gives us \(7y = 3\times14\), which simplifies to \(7y = 42\). Then, dividing both sides by 7, we get \(y=\frac{42}{7}=6\).

Answer:

For Monday, the number of mosquitoes is 35. For Tuesday, the number of flies is 6. So the completed table values are: Monday - Mosquitoes: 35; Tuesday - Flies: 6.