SOLUTION: This is the closest subject I could find, so, here goes.The real subject is digit problems. ::A number between 300 and 400 is forty times the sum of its digits. The tens digit i

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Question 114581This question is from textbook
: This is the closest subject I could find, so, here goes.The real subject is digit problems.
::A number between 300 and 400 is forty times the sum of its digits. The tens digit is 6 more than the units digit. Find the number.This question is from textbook

Answer by jim_thompson5910(21684) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=tens digit, y=units digit

Since "The tens digit is 6 more than the units digit" we get x=y%2B6

Since the number is between 300 and 400, we know that the number must be of the form 300%2B10%2Ax%2By and since the number is 40 times the sum of the digits, we then have the equation

300%2B10%2Ax%2By=40%283%2Bx%2By%29


300%2B10%2Ax%2By=120%2B40x%2B40y Distribute


300%2B10%28y%2B6%29%2By=120%2B40%28y%2B6%29%2B40y Now plug in x=y%2B6


300%2B10y%2B60%2By=120%2B40y%2B240%2B40y Distribute again


360%2B11y=360%2B80y Combine like terms


360=360%2B80y%2B11y Subtract 11y from both sides


360-360=80y%2B11y Subtract 360 from both sides



0=91y Combine like terms

0%2F91=y Divide both sides by 91

So the units digit is 0


This means the tens digit is:

x=0%2B6=6

So we have:

tens digit: 6 , ones digit: 0

-----------------------------------------
Answer:

So our number is 360


Check:

Notice if we add the digits of 360, we get

3+6+0=9


Now multiply the sum by 40


9*40=360


which is our number. So our answer is verified