the sum of three numbers is 68. The largest number is 6 less than twice the smallest

Question

find the three numbers

Answer 1

Numbers A, B and C. Let C be the largest number then C=2A-6 if A is the smallest.

A+B+C=68, so A+B+2A-6=68 and 3A+B=74. So B=74-3A and B is bigger than A and smaller than C.

C is bigger than A and B, so 2A-6>A therefore A>6 and 2A-6>74-3A, so 5A>80 and A>16, making C>26.

B=74-3A. Since A>16, 3A>48, so B<74-48 or B<26.

Now we have A>16, A<B<26<C, C>26 and A+B+C=68. Try A=17 and C=34-6=28, so B=68-45=23.

If A=18, C=30 and B=20; but if A=19, C=32 and B<A at 17, which violates the requirements.

So we seem to have two integer solutions: 17, 23, 28 and 18, 20, 30.