## Math Forum - Problem of the Week

### Fish Farm I

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Fish Farm I

### A Fishy Family

For their birthday, the Carp triplets received 26 tropical fish: 13 females and 13 males. They discussed ways to divide the fish among their three tiny backyard ponds.

Angel said, "I want the same number of male and female fish in my pond."

"Okay," said Molly. "I want three times as many males as females in my pond."

"Then I want twice as many females as males in my pond," Gar replied.

Is there a way to put all 26 fish into those three ponds, while giving each triplet what he or she wants? Use the applet to explore this question.

### Questions

1. How many male fish and female fish does each triplet get in his or her pond? Describe the work you did to find the solution. (Sample questions you can answer: Into which pond did you put fish first? How many fish of each kind went into that pond? Why? What was your next step? How were you sure a pond had the correct ratio?)

2. Given the 13 males and 13 females, what are ALL the possible numbers of male and female fish that would satisfy the ratio of 1 male to 2 female fish in Gar's pond? Explain why these different amounts are equivalent to the ratio 1:2.

Bonus: Explain why all possible answers in question 2 result in the same pie graph for Gar's pond.

Extension Problems (not to be submitted):

1. Find a different way to distribute all 26 fish among the three ponds in the correct ratios.

2. Distribute the fish into the three ponds such that only 1 female fish is left in the large tank. Is there more than one way to distribute the fish and achieve the target ratios?

3. Distribute the fish into the three ponds such that only 1 male fish is left in the large tank. Is there more than one way to distribute the fish and achieve the target ratios?

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