five consecutive numbers having sum of 120,
product of 1st and 3rd and product of 2nd and4th have a ratio of 20/21. what are they

Question

five consecutive numbers having sum of 120,
product of 1st and 3rd and product of 2nd and4th have a ratio of 20/21. what are they

anonymous · Answer

let numbers are x , x+1,x+2,x+3 and x+4
now as your problem says x + x+1+x+2+x+3 +x+4 =120
solve and get x........and x+4

solomonzelman · Answer

You only need the 1st sentence.

lets call the MIDDLE term "x", so the 2 before would be  x-2  and  x-1, and the 2 after would be  x+1  and  x+2.

Write it out,
$$(x-2)+(x-1)+x+(x+1)+(x+2)=120$$ solve,$$x-2+x-1+x+x+1+x+2=120$$
$$5x=120$$

Can you tell me the five numbers now?
(hint: the middle term is the x that you are solving for)

anonymous · Answer

middle term is=120/5=24
terms are 24-2,24-1,24,24+1,24+2
note these do not satisfy second condition.

solomonzelman · Answer

Well then... but they are CONSECUTIVE and add up to 120, so these are the only possible numbers.