SOLUTION: Shane added a number to one-sixth. Chris subtracted the same number from one and two-thirds. They each got the same answer. What is the number? I cannot figure this out. I have

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Shane added a number to one-sixth. Chris subtracted the same number from one and two-thirds. They each got the same answer. What is the number? I cannot figure this out. I have       Log On


   

Question 787247: Shane added a number to one-sixth. Chris subtracted the same number from one and two-thirds. They each got the same answer. What is the number?
I cannot figure this out. I have tried for 2 days. My Dad has tried to help me. We both don't get it
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"Shane added a number to one-sixth" translates to x+%2B+1%2F6

"Chris subtracted the same number from one and two-thirds" translates to 1%262%2F3+-+x and because 1%262%2F3+=+%281%2A3%2B2%29%2F3+=+5%2F3. So this means that 1%262%2F3+-+x is the same as 5%2F3+-+x

-------------------------------------------------------

"They each got the same answer." means that the two expressions are equal, so this means

x+%2B+1%2F6+=+5%2F3+-+x

x+%2B+1%2F6++%2B+x=+5%2F3 Add x to both sides.

x++%2B+x=+5%2F3+-+1%2F6 Subtract 1/6 from both sides.

x++%2B+x=+10%2F6+-+1%2F6 Multiply 5/3 by 2/2.

2x=+9%2F6 Combine like terms.

2x=+3%2F2 Reduce

x=+%283%2F2%29%2A%281%2F2%29 Multiply both sides by 1/2 to isolate x

x=+%283%2A1%29%2F%282%2A2%29

x=+3%2F4

Therefore, the number is 3%2F4