Solving the Mystery: How Many Yellow Jelly Beans Were in the Dish?

Imagine you’re at a party and you come across a dish filled with red and yellow jelly beans. You notice that the ratio of red to yellow jelly beans is 3:4. Greg, a fellow party-goer, eats 3 red jelly beans and 6 yellow ones, and now the ratio is 4:5. This sparks a question in your mind: how many yellow jelly beans were originally in the dish? This might seem like a simple question, but it’s actually a fun and interesting problem in ratio and proportion. Let’s dive in and solve this jelly bean mystery!

Understanding the Problem

First, let’s understand the problem. We know that the ratio of red to yellow jelly beans was 3:4 before Greg started eating. This means that for every 3 red jelly beans, there were 4 yellow ones. After Greg ate some jelly beans, the ratio changed to 4:5. This means that for every 4 red jelly beans left, there were 5 yellow ones. The question is, how many yellow jelly beans were there at the start?

Setting Up the Equations

To solve this problem, we need to set up two equations based on the information given. Let’s denote the number of red jelly beans at the start as R and the number of yellow jelly beans as Y. The first equation, based on the initial ratio, is R/Y = 3/4. The second equation, based on the ratio after Greg ate some jelly beans, is (R-3)/(Y-6) = 4/5.

Solving the Equations

Now, we need to solve these equations. We can start by cross-multiplying the first equation to get 4R = 3Y. Then, we can cross-multiply the second equation to get 5(R-3) = 4(Y-6). Simplifying the second equation gives us 5R – 15 = 4Y – 24. Substituting 4R for 3Y in this equation gives us 5R – 15 = 4(4R/3) – 24. Solving this equation gives us R = 27.

Finding the Number of Yellow Jelly Beans

Now that we know the number of red jelly beans at the start, we can find the number of yellow jelly beans. Substituting R = 27 into the first equation gives us 4*27 = 3Y, which simplifies to Y = 36. So, there were 36 yellow jelly beans in the dish at the start.

Conclusion

So, the mystery is solved! There were 36 yellow jelly beans in the dish at the start. This problem is a great example of how ratios and proportions can be used to solve real-world problems. So, the next time you come across a dish of jelly beans, you’ll know how to solve the mystery!