Questions: Mike caught 22 fish this week, or 3 2/3 rds times as many as last week. How many fish did Mike catch last week?

Solution Steps

To find out how many fish Mike caught last week, we need to set up an equation based on the information given. We know that the number of fish caught this week (22) is \(3 \frac{2}{3}\) times the number of fish caught last week. We can convert \(3 \frac{2}{3}\) to an improper fraction and then solve for the number of fish caught last week.

Mike caught 22 fish this week, which is \(3 \frac{2}{3}\) times the number of fish he caught last week. We need to find out how many fish he caught last week.

Convert \(3 \frac{2}{3}\) to an improper fraction: \[ 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \]

Let \(x\) be the number of fish Mike caught last week. According to the problem: \[ 22 = \frac{11}{3} \times x \]

To find \(x\), we solve the equation: \[ x = \frac{22}{\frac{11}{3}} = 22 \times \frac{3}{11} = 2 \times 3 = 6 \]

Final Answer