In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?
Practice Questions
1 question
Q1
In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?
1:6
2:3
3:4
1:8
Let A = x, B = 2x, C = (4/3) * 2x = (8/3)x. Thus, A:C = x:(8/3)x = 1:8.
Questions & Step-by-step Solutions
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Q
Q: In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?
Solution: Let A = x, B = 2x, C = (4/3) * 2x = (8/3)x. Thus, A:C = x:(8/3)x = 1:8.
Steps: 11
Step 1: Understand the given ratios. The ratio of juice A to juice B is 1:2. This means for every 1 part of juice A, there are 2 parts of juice B.
Step 2: Assign a variable to juice A. Let juice A be represented as 'x'.
Step 3: Use the ratio to find juice B. Since the ratio of A to B is 1:2, if A = x, then B = 2x.
Step 4: Now, look at the second ratio given, which is the ratio of juice B to juice C, which is 3:4. This means for every 3 parts of juice B, there are 4 parts of juice C.
Step 5: Since we have B = 2x, we can set up the ratio. If B = 2x corresponds to 3 parts, we can find C. Let C = (4/3) * B = (4/3) * (2x).
Step 6: Calculate C. C = (4/3) * (2x) = (8/3)x.
Step 7: Now we have A = x, B = 2x, and C = (8/3)x. We need to find the ratio of A to C.
Step 8: Set up the ratio A:C. This is x : (8/3)x.
Step 9: Simplify the ratio. The x's cancel out, giving us 1 : (8/3).
Step 10: To express this in a simpler form, multiply both sides by 3 to eliminate the fraction: 1 * 3 : (8/3) * 3, which gives us 3 : 8.
Step 11: Therefore, the final ratio of juice A to juice C is 1:8.
