A, b,c are positive integers. a: b = 3: 8 b: c = 6: 11 work out the smallest possible value of a+b+c

Work out the a:b:c ratio.

b is present in both ratios, find first the LCM of 8 and 6, which is 24.

Multiply a:b=3:8 by 3 to get a:b=9:24

Similarly, multiply b:c=6:11 by 4 to get b:c=24:44

Then we conclude

a:b:c=9:24:44

Since there is no common factor among the three numbers, this is the simplest ratio possible.

If a,b and c are integers, the smallest values for a,b and c are 9,24,44.

Add up the three numbers to get the least value of a+b+c=77.

The smallest possible value of a+b+c is equal to 77 where a, b, and c are 9, 24, and 44 respectively and it can be determine by using arithmetic operations.

Given :

The following steps can be used to determine the value of (a+b+c) :

Step 1 - b present in both the ratios therefore first find the LCM of 6 and 8.

The LCM of 6 and 8 is 24.

Step 2 - Now, multiply numerator and denominator of ratio (1) by 3.

Step 3 - Now, multiply numerator and denominator of ratio (2) by 4.

For the smallest possible value of a+b+c the value of a, b, and c are 9, 24, and 44.

Therefore, the smallest possible value of a+b+c is equal to 9+24+44 = 77.

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