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?
Practice Questions
1 question
Q1
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?
1:3
1:4
2:3
3:4
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.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
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.
Steps: 9
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.
