SOLUTION: Hi! I need some help. Sorry for the trouble. My question is: A number is four times another number. Six times the smaller number plus half of the larger number equals 212. Find

Question 654600: Hi! I need some help. Sorry for the trouble. My question is:
A number is four times another number. Six times the smaller number plus half of the larger number equals 212. Find the numbers.
I tried to solve it myself but I couldn't. I thought that since the larger number is four times the smaller number, and six times the smaller number plus half the larger equals 212, then 8 times the smaller number would be 212. So the smaller number is 26.5. This means that the larger number is 106. Half of 106 is 53. 26.5 times 6 is 159. 159 plus 53 is 212. But, for some reason, my answers don't match the answer key at the back of my book. Am I doing something wrong? And if so, what?
Thank you in advance, whoever you are for reading this problem and trying to solve it!
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

 

Hi,

Best to Set it Up and Solve it Algebraicly

A number is four times another number. 

Six times the smaller number plus half of the larger number equals 212

Question states***

     || ,   Substituting for y...

  

 

   

     x = 212/8 = 26.5   and y = 106

and...

  

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