Mathematics Challenge | Learn how to find the value of 999/(X+888) | Math Olympiad Preparation

Learn how to solve this given rational if-then problem by using basic algebra and manipulations. Find the value of 999/(X+888) if 666/(X+777)=888. Calculators Not Allowed

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Mathematics Challenge | Learn how to find the value of 999/(X+888) | Math Olympiad Preparation

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[sy]

Thank you for explaining. The final answer should be (3996/447 =) 1332/149.

[Copernicusfreud]

I did the long division and long multiplication to get the answer in the video, except I divided the final numerator and denominator by 3 to get 1332 / 149.

[allanflippin]

I appreciate the lesson on substitution, but doesn't that approach actually make things more complicated? Suppose one replaces the "888" with "888/1" then cross multiply the two fractions. That will give you 666 = 888 * (X + 777), Then X + 777 = 666/888 or X = 3/4 - 777. Substituting for X in the second equation, you get 999 / (111 + 3/4), then simplify with the method you showed.

[ernestboston]

I did it in far fewer steps:

666/ (x + 777) = 888
its easy to see that a string of 6's over a string of 8's is 3/4
666/888 = 3/4 = x + 777, so x = -776.25
2 nd part
999/(x + 888) = ?
999/(888 - 776.25) = 999/111.75
111 3/4 = 444/4 + 3/4 = 447/4
999 * 4/447 = 3*333*4/3*149 = 333*4/149 = 1332/149

When I first looked at the problem, I thought 'wow!' But then I quickly evaluated the first equation in my head and then realized it was then just a matter of dealing with improper fractions.

[HappyFamilyOnline]

Excellent explanation👍👍
Thanks for sharing😊😊

[plamenpenchev]

It would be easier to transform eqs. as
6/(y + 7) = 888
9/(y + 8) = ?,
where y = x/111.
Reverse the first, add 1/6, then multiply by 2/3, reverse again and you obtain the searched value as
3/2*1/(1/888 + 1/6)

[ytlongbeach]

pretty good, but you can see the answer can be simplified even more. the numerator and denominator are both divisible by 3, which you can quickly see because the sum of the digits of each of these numbers is divisible by 3. hence, the final answer should be 1332/149.

[miguelgnievesl]

That result can be further simplified. 1332/149

[bigm]

A really great way to approach the problem. Thanks Professor!

[asamadawais]

Why 0.25 / 0.5 = 0.5? Pls tell reasons in mathematics language. Thx!!!

[igvarn]

I mentally counted 999/111, 75, can be seen ~9

[marcuslatrell]

I got it like this:

666/x=888
666=888x
666/888=x
3/4=x
777-776.25=3/4
Therefore, the x in the vid is - 776.25

[octobrerouge]

Technique cette exercice le raisonnement me plaît merci 🙏

[vijaysimha]

Last expression
Both numerator and denominator are divisible by 3 and can be reduced further.