Answer:
We can use ratios to set up a system of equations and solve for a, b, and c. Since a:b = 3:8, we can write:
a = 3x
b = 8x
Similarly, since b:c = 6:11, we can write:
b = 6y
c = 11y
Now we have two expressions for b, so we can set them equal to each other and solve for y:
8x = 6y
y = 4x/3
Substituting y back into the expression for c, we get:
c = 11y = 44x/3
To find the smallest possible values of a, b, and c, we want to choose values of x that are as small as possible while still being positive integers. Since x must be a multiple of 3 (because a = 3x is a multiple of 3), let's try x = 3. Then we get:
a = 3x = 9
b = 8x = 24
c = 44x/3 = 44
So the smallest possible values of a, b, and c are 9, 24, and 44, respectively.
Explanation: