The ratio of w to x is 4:3, of y to z is 3:2 and of z to x is 1:6. What is the ratio of w to y?
w/y = (w/x)(x/z)(z/y) = (4/3)(6/1)(2/3) = 16/3
To find the ratio of w to y, we need to establish a common variable between them. Let's find the relationship between w, x, y, and z using the given information:
1. The ratio of w to x is 4:3.
2. The ratio of y to z is 3:2.
3. The ratio of z to x is 1:6.
To establish a common variable, let's find the ratio of z to y using the given ratios:
Since the ratio of z to x is given as 1:6, we can say that the ratio of x to z is 6:1 (inverse ratio).
Multiplying the ratios of y to z (3:2) and x to z (6:1), we get the ratio of y to x as 18:2.
To establish another common variable, we can find the ratio of y to w:
Since the ratio of w to x is given as 4:3, we can say that the ratio of x to w is 3:4 (inverse ratio).
Multiplying the ratios of y to x (18:2) and x to w (3:4), we get the ratio of y to w as 54:8.
Simplifying this ratio, we have:
y:w = 54:8
Therefore, the ratio of w to y is 8:54, which can also be simplified to 4:27.
To find the ratio of w to y, we can use the given ratios and a combination of ratio properties.
First, let's find the ratio of z to y. We have the ratio of y to z as 3:2. By taking the reciprocal of this ratio, we get the ratio of z to y, which is 2:3.
Next, we need to find the ratio of x to w. Given that the ratio of w to x is 4:3, if we switch the positions of w and x, we get the ratio of x to w, which is 3:4.
Now, let's combine the ratios we have obtained. We have:
- z:y = 2:3
- x:w = 3:4
To find the ratio of w to y, we can combine the ratios z:y and x:w. We multiply the corresponding terms:
- (z:y) * (x:w) = (2:3) * (3:4)
Multiplying the numerators together (2 * 3) and the denominators together (3 * 4), we get:
- (z:y) * (x:w) = 6:12
Since both 6 and 12 are divisible by 6, we can simplify the ratio by dividing both terms by 6:
- (z:y) * (x:w) = 1:2
Therefore, the ratio of w to y is 1:2.