SOLUTION: 27. A number is between 30 and 40. If the number is divided by the sum of the digits, the quotient is 4. Find the number.

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Question 927832: 27. A number is between 30 and 40. If the number is divided by the sum of the digits, the quotient is 4. Find the number.
Found 2 solutions by ptfile, MathTherapy:
Answer by ptfile(81)   (Show Source): You can put this solution on YOUR website!
Let 10t+u = The Number
t+u = The Digits
If the number is divided by the sum of the digits, the quotient is 4.
10t+u
----- = 4
t+u
Multiply each side by t+u
10t+u=4(t+u)
10t+u=4t+4u
6t=3u
Divide the whole equation by 3
2t=u
A number is between 30 and 40.
30 < 10t+2t < 40
30 < 12t < 40
30/12 < t < 40/12
2.5 < t < 3.33
t = 3
u = 6
Since the unit digit is twice the tens digit and should be in a range between
30 and 40, the only number applicable with this boundaries is 36.
Check
3+6=9
36/9=4


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

27. A number is between 30 and 40. If the number is divided by the sum of the digits, the quotient is 4. Find the number.
Since number is between 30 and 40, its tens digit MUST be 3

Let units digit be U

Then number is: 30 + U

Sum of digits: 3 + U

Based on info., we get: 

4(3 + U) = 30 + U -------- Cross-multiplying

12 + 4U = 30 + U

4U – U = 30 – 12

3U = 18

U, or units digit = , or 6

Number: 

You can do the check!! 

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