Question

A jar contains red, blue, and green marbles. The ratio of red to blue marbles is 3:4, and the ratio of blue to green marbles is 2:5. What is the ratio of red to green marbles?

• A. 3:10
• B. 3:5
• C. 6:20
• D. 8:15
• E. 15:8

Hint:

When combining ratios like A:B and B:C, think of it as finding a common denominator. The middle term 'B' is the key. Once the 'B' values are the same, you can write the full A:B:C ratio.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
We are given two separate ratios that share a common element (blue marbles). To find the ratio between the other two elements (red and green), we must first create a continuous ratio by making the value of the common element the same in both original ratios.
Step 2: Key Formula or Approach:
Let the ratios be R:B = 3:4 and B:G = 2:5.
Find the Least Common Multiple (LCM) of the terms for B (which are 4 and 2).
Adjust each ratio to match this common value.
Combine them into a single R:B:G ratio.
Step 3: Detailed Explanation:
The given ratios are:
\[ R : B = 3 : 4 \]
\[ B : G = 2 : 5 \]
The values corresponding to B are 4 and 2. The LCM of 4 and 2 is 4.
The first ratio already has B as 4, so we leave it: \(R : B = 3 : 4\).
In the second ratio, we need to change B from 2 to 4. We do this by multiplying both parts of the ratio by 2:
\[ B : G = (2 \times 2) : (5 \times 2) = 4 : 10 \]
Now both ratios have a common B value of 4:
\[ R : B = 3 : 4 \]
\[ B : G = 4 : 10 \]
We can now combine these into a single ratio:
\[ R : B : G = 3 : 4 : 10 \]
The question asks for the ratio of red to green marbles (R:G). From our combined ratio, we can see:
\[ R : G = 3 : 10 \]
Step 4: Final Answer:
The ratio of red to green marbles is 3:10, which corresponds to option (A).