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?
To find the ratio of w to y, we need to establish a common variable between w and y. We can do this by referring to the ratios involving the variables w, x, y, and z.
Let's examine the given ratios:
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.
We can use ratio equivalence to compare the ratios involving z:
2. The ratio of y to z is 3:2.
3. The ratio of z to x is 1:6.
By multiplying the second ratio by 3, we can make the z terms equivalent:
2 × 3: z × 3
6: 3z
Now, we can compare the ratio of w to x to the ratio of z to x:
1. The ratio of w to x is 4:3.
3. The ratio of z to x is 1:6.
We can set up an equation to relate the ratios involving x:
4:3 = 1:6
To make the ratios equal, we need to multiply both sides of the second ratio by 4:
1 × 4: 6 × 4
4: 24
Therefore, we have:
4:3 = 4:24
Now we can compare the ratios involving w and y:
4:24 (w:x) and 6:3z and 3:2 (y:z).
To combine the ratios, we need to relate w and y using the common variable z:
4:24 (w:x), 6:3z, and 3:2 (y:z).
By multiplying the first ratio by 6, the second ratio by 8, and the third ratio by 4, we can make the z terms equivalent:
4 × 6: 24 × 6,
6 × 8: 3z × 8,
3 × 4: 2 × 4z.
This gives us:
24:144 (w: x),
48: 24z, and
12: 8z.
Now we can see that the ratio of w to y is:
24:12.
Simplifying this ratio by dividing both sides by 12 gives us:
2:1.
Therefore, the ratio of w to y is 2:1.