SOLUTION: 3) The units digit is 3 times more the tens digit. When the digits are reversed, the new number is 54 more than the original. 4)The units digit is 3 times the tens digit. The n

Algebra ->  Equations -> SOLUTION: 3) The units digit is 3 times more the tens digit. When the digits are reversed, the new number is 54 more than the original. 4)The units digit is 3 times the tens digit. The n      Log On


   

Question 448333: 3) The units digit is 3 times more the tens digit. When the digits are reversed, the new number is 54 more than the original.
4)The units digit is 3 times the tens digit. The number is 12 more than 9 times the tens digit.

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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started. If you need more help, then repost.

# 3


Let u = units digit and t = tens digit


So the original number is then 10t%2Bu. The reversed digit number is 10u%2Bt (swap u and t). Ex: if t = 5 and u = 9, then the original number is 59 and the swapped number is 95.


Since "The units digit is 3 times more the tens digit", we know that u=3t (ie multiply the tens digit t by 3 to get the units digit u).


Now "When the digits are reversed, the new number is 54 more than the original", this means that 10u%2Bt=10t%2Bu%2B54


10u%2Bt=10t%2Bu%2B54 Start with the given equation.


10%283t%29%2Bt=10t%2B3t%2B54 Plug in u=3t (ie replace EVERY "u", without quotes, with "3t", without quotes)


30t%2Bt=10t%2B3t%2B54 Multiply


31t=10t%2B3t%2B54 Combine like terms on the left side.


31t=54%2B13t Combine like terms on the right side.


31t-13t=54 Subtract 13t from both sides.


18t=54 Combine like terms on the left side.


t=%2854%29%2F%2818%29 Divide both sides by 18 to isolate t.


t=3 Reduce.


So the tens digit is 3. Because we know that u=3t, we can plug this into that equation to get u=3%283%29=9. So the units digit is 9


So the original number is 39. The new swapped number is 93. Notice how 93 is 54 more than 39 (ie 39+54 = 93)


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# 4

Use the same basic strategy to solve this problem. Let me know if you still need help.