a,b,c are positive integers such that a:b=7:9 and b:c=12:7 . What is the smallest possible value of a ?
To find the smallest possible value of a, we need to compare the ratios between a and b, and b and c. Let's find the common ratio between them.
Given: a:b = 7:9 and b:c = 12:7.
To find the ratio between a and c, we can combine the given ratios:
(a:b) * (b:c) = (7:9) * (12:7).
Multiplying the ratios, we get:
a:c = (7 * 12) : (9 * 7).
a:c = 84:63.
To simplify the ratio, we divide both sides by the greatest common divisor (GCD) of 84 and 63, which is 21:
a:c = (84 ÷ 21) : (63 ÷ 21).
a:c = 4:3.
Therefore, the smallest possible value of a is 4.