In a mixture of three liquids, the ratio of liquid X to Y is 1:2, and the ratio

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Question: In a mixture of three liquids, the ratio of liquid X to Y is 1:2, and the ratio of Y to Z is 3:4. What is the ratio of X to Z?

Options:

Correct Answer: 1:4

Solution:

From X:Y = 1:2 and Y:Z = 3:4, we can express X:Z as 1:(2*(4/3)) = 1:8/3 = 1:4.

In a mixture of three liquids, the ratio of liquid X to Y is 1:2, and the ratio of Y to Z is 3:4. What is the ratio of X to Z?

In a mixture of three liquids, the ratio of liquid X to Y is 1:2, and the ratio of Y to Z is 3:4. What is the ratio of X to Z?

Step 1: Understand the given ratios. We have two ratios: X:Y = 1:2 and Y:Z = 3:4.
Step 2: Rewrite the first ratio (X:Y) in terms of Y. If X = 1 part, then Y = 2 parts.
Step 3: Rewrite the second ratio (Y:Z) in terms of Y. If Y = 3 parts, then Z = 4 parts.
Step 4: Find a common value for Y in both ratios. The first ratio has Y as 2 parts, and the second ratio has Y as 3 parts. To make them the same, we can multiply the first ratio by 3 and the second ratio by 2.
Step 5: After multiplying, we get X:Y = 3:6 and Y:Z = 6:8.
Step 6: Now we can express the ratios together. From X:Y = 3:6 and Y:Z = 6:8, we can see that Y is 6 parts in both ratios.
Step 7: Now we can find the ratio of X to Z. Since X = 3 parts and Z = 8 parts, we can write the ratio as X:Z = 3:8.
Step 8: To express this in the simplest form, we can divide both parts by 3, which gives us X:Z = 1:(8/3).
Step 9: Finally, we can convert 8/3 into a simpler ratio. This gives us X:Z = 1:4.

Ratios – Understanding and manipulating ratios to find relationships between different quantities.
Proportions – Using proportions to relate different ratios and derive new ones.