Question

a, b and c are positive integers.

a:b=3:8 and b:c=6:11
work out the smallest possible value of a+b+c

Answer 1

a : b => 5 : 6 and b : c => 8 : 11

We need the lowest common multiple of 6 and 8, which is 24

Hence, a : b => 20 : 24 and b : c => 24 : 33

i.e. a : b : c => 20 : 24 : 33

Then, lowest value of a + b + c = 77

Answer 2

Answer:

The smallest value is $77$

Step-by-step explanation:

It is given that $a,b,c$ are positive integers.

$a:b=3:8$

and

$b:c=6:11$

In first ratio, value of $b=8$ and other other has $b=6$

LCM (lowest common multiple of $6,8=24$)

So,

$a:b=3*3:8*3=9:24$

Similarly,

$b:c=6*4:11*4=24:44$

So,

$a:b:c=9:24:44$

The smallest value is obtained by adding three of them.

$9+24+44=77$

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