Question 114581
Let x=tens digit, y=units digit


Since "The tens digit is 6 more than the units digit" we get {{{x=y+6}}}


Since the number is between 300 and 400, we know that the number must be of the form {{{300+10*x+y}}} and since the number is 40 times the sum of the digits, we then have the equation


{{{300+10*x+y=40(3+x+y)}}}



{{{300+10*x+y=120+40x+40y}}} Distribute



{{{300+10(y+6)+y=120+40(y+6)+40y}}} Now plug in {{{x=y+6}}}



{{{300+10y+60+y=120+40y+240+40y}}} Distribute again



{{{360+11y=360+80y}}} Combine like terms



{{{360=360+80y+11y}}} Subtract 11y from both sides



{{{360-360=80y+11y}}} Subtract 360 from both sides




{{{0=91y}}} Combine like terms


{{{0/91=y}}} Divide both sides by 91


So the units digit is 0



This means the tens digit is:


{{{x=0+6=6}}}


So we have:


tens digit: 6 , ones digit: 0


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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