If x : y = \(\frac{1}{4} : \frac{3}{8}\) and y : z = \(\frac{1}{3} : \frac{4}{9}\), find x : z
Answer Details
To find x : z, we need to have a common ratio between x, y, and z. We can use the given ratios to find a common ratio involving all three.
Since x : y = 1/4 : 3/8, we can simplify this ratio by multiplying both terms by 8 to get:
x : y = 2 : 3
Similarly, since y : z = 1/3 : 4/9, we can simplify this ratio by multiplying both terms by 3 to get:
y : z = 1 : 4/3
Now we have a common ratio of y between the two ratios. We can use this common ratio to find x : z by multiplying the two simplified ratios:
x : y = 2 : 3
y : z = 1 : 4/3
Multiplying these ratios gives:
x : z = (2/3) * (1/(4/3)) = 2/4 = 1/2
Therefore, x : z = 1 : 2.
In summary, x : z = 1 : 2.