Final answer:
To find the smallest possible value of a+b+c, we need to find the values of a, b, and c. From the given ratios, we can set up the equations and solve for a, b, and c. The smallest possible value of a+b+c is approximately 1.852.
Step-by-step explanation:
a:b = 3:8 and b:c = 6:11.
To solve for a, b, and c, we need to first find the common ratio between a and b, and between b and c. We can do this by finding the least common multiple (LCM) of the denominators in the ratios. In this case, the LCM of 8 and 11 is 88.
Next, we can multiply the ratios by the appropriate coefficients to get whole numbers. We can use the coefficients 11 and 8 for the first equation and 8 and 6 for the second equation. Multiplying the ratios, we get a:b = 33:88 and b:c = 48:66.
Now, we can substitute the values back into the original equations to find the values of a, b, and c. Solving for a, we get a = 33/88. Solving for b, we get b = 48/66. Solving for c, we get c = 66/88.
To find the smallest possible value of a+b+c, we add the values of a, b, and c. Plugging in the values, we get (33/88) + (48/66) + (66/88) = 0.375 + 0.727 + 0.75 = 1.852. Therefore, the smallest possible value of a+b+c is approximately 1.852.