SOLUTION: Hi The digits of a 2 digit number differ by 4. When the digits are reversed the reversed number is 75% greater than the original number. What is the number.

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Question 1205625: Hi
The digits of a 2 digit number differ by 4. When the digits are reversed the reversed number is 75% greater than the original number. What is the number.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
t, tens digit
u, the ones or units digit

If these are t for tens and t+4 for units
then 10%28t%2B4%29%2B1%2At=10t%2B%28t%2B4%29%2B%283%2F4%29%2810t%2Bt%2B4%29
10t%2B40%2Bt=10t%2Bt%2B4%2B%283%2F4%29%2810t%2Bt%2B4%29
11t%2B40=11t%2B4%2B%283%2F4%29%2811t%2B4%29
40-4=%283%2F4%29%2811t%2B4%29
4%2A36=33t%2B12
33t=4%2A36-12
33t=132
3t=12
t=4

Number originally, 48


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(problem description could be worked on further)

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


When the digits are reversed, the new number is greater than the original number. Therefore in the original number the tens digit is the smaller digit. So

let x = tens digit
then x+4 = units digit

The original number is 10(x)+(x+4) = 11x+4
The new number is 10(x+4)+x = 11x+40

The new number is 75% greater than the original number -- i.e. 7/4 as large:

11x%2B40=%287%2F4%29%2811x%2B4%29
44x%2B160=77x%2B28
132=33x
x=4

The original number has tens digit x=4 and units digit x+4=8.

ANSWER:48

This problem also allows for a solution using logical reasoning and simple arithmetic, which is very good mental exercise.

Since the new number is larger than the original number and the digits differ by 4, the possible answers are 15, 26, 37, 48, and 59.
The new number is 75% greater than the original, which means it is 7/4 of the original number.
Since the digits are whole numbers, that means the original number is a multiple of 4.
The only one of the possible answers that is a multiple of 4 is 48.

ANSWER: 48