The ratio of the number of goldfish to guppy in a fish tank is 5:4. After 3 guppies died, the ratio of the number of goldfish to guppy is 4:3. What was the total number of angelfish and clownish in the aquarium at first? [2]
How to solve this question?
First of all, the student has to identify the topic. In this question it is clear cut, and the topic in question is obviously ratio.
Next, what technique to use? Ratio is a concept introduced in P5, and as such, students are typically motivated to use models. However, the ratios given will make modeling difficult, as the numbers are very close to one another, and there has been a subtraction somewhere down the road.
So, how do we address this issue? For most questions on ratio, I would use my ratio method! The method is simplistic and easy to visualize.
Before: After:
GF:GP GF:GP
5:4 4:3
Note that there is one variable that remains constant! That is the value of the goldfish. Since the total goldfish does not change, we can hold that value constant. This means, that the value of the goldfish before and after will remain the same. Based on what the student knows about ratio, the student must recall that you can expand a ratio beyond its simplest form. Since we want the ratio or the units of goldfish to be uniform for before and after, we shall expand by multiplying the ratio in before by x4, and multiplying the ratio in after by x5.
Before: After:
GF:GP GF:GP
20:16 20:15
As you can see, now the ratio of goldfish is uniform, and it makes it so much easier to compare! The guppies have decreased from 16 units to 15 units, and goldfish remains the same, this checks out with regard to the question. Next, the question says that 3 guppies died, so the decrease of 1unit has to be representing the death of the 3 guppies!
Therefore, 1 unit for both ratio represents 3, and since there are 20+16=36 units at first, the answer is simply 36×3=108!
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Mr Y.S Pang, B.Eng(hons)NUS, Math tutor at Singapore Learner and Concept Learning
