A problem by Dick He

Level pending

y-x=-10
zy^2=x+56
y<w<x<z
yz=x+22
y=w-3
x-5=w+y
What is w+x+y+z=?
NOTE: The first solution, my solution, is a bit out-dated because I modified this question so it would become even more difficult. Also if you find an actual answer that is considered wrong please leave it in the solution "chatroom" and I will add another equation to focus down to the only solution I have in mind.


The answer is 36.

Dick He by Dick He , 20, USA

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1 solution

Dick He
Jan 14, 2014

First look at the last 2 equations. For w on the last one you can substitute y+3 for w when you look at the above equation. Now the last equation becomes x-5=2y+3 which you can turn into x=2y+8. Now you can substitute x in the top equation as 2y+8. y-2y-8 turns in to -y-8=-10-> y=2. Now you know y go to the equation 4 and complete 16+1=z or 17. Go to the fifth and get 5=w. Now to any equation that has x and you should be able to acquire w.

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Now I just modified it here is how you do it. Get y and go to equations 2 and 4. You will notice 4z=x+56 but 2z only equals x+22. You can see 2z=34 using reasoning and logic. (because 2 more z makes the one side of the equation worth 34 more. Now you still get z=17. Also you can not easily find w after y but you have to do it after z. Lastly, I didn't say in my first solution, you have to add w+x+y+z to get 36, 2+5+12+17

Dick He - 7 years, 4 months ago

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