If A: B = 15 : 16, B : C = 8 : 25, C : D = 20 : 9, then find A: D.

Given:
A: B = 15 : 16,
B : C = 8 : 25,
C : D = 20 : 9
Solution:
we need to make the 'B' and 'C' values equal in all ratios.
Let's start with B:
A : B = 15 : 16
B : C = 8 : 25
To make B equal in both ratios,

we can multiply the first ratio by 8 and the second ratio by 16:

A : B = 120 : 128
B : C = 128 : 400
Now, we can combine these ratios:
A : B : C = 120 : 128 : 400
Next, let's consider C : D:
C : D = 20 : 9
To make C equal in both ratios, we can multiply this ratio by 20:
C : D = 400 : 180
Now, we can combine all three ratios:
A : B : C : D = 120 : 128 : 400 : 180
To simplify this ratio, we can divide all numbers by their greatest common divisor, which is 4:
A : B : C : D = 30 : 32 : 100 : 45
A : D = 30 : 45
 = 2 : 3
Alternate Solution:
A : B = 15 : 16
B : C = 8 : 25 = 16 : 50
A : B : C = 15 : 16 : 50
A : B : C = 30 : 32 : 100
C : D = 20 : 9 = 100 : 45
A : B : C : D = 30 : 32 : 100 : 45
A : D = 30 : 45
A : D = 2 : 3​​