SOLUTION: A number is between 20 and 30 and is three times the sum of its digits. What is the number?

Question 829757: A number is between 20 and 30 and is three times the sum of its digits. What is the number?

Found 3 solutions by josgarithmetic, edjones, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Two-digit number, .
Expect the number and .
We must expect only Natural Numbers for x and y, so if graphing, these must be only in quadrant 1.

The other part of the description:
.
Simplify.
3x+3y=10x+y
3y=7x+y
2y=7x

Next plan is that we can plot that line. Intercepts are (0,0) only. The equation can be shown as ; and because of the inequalities expected above, and .

The easiest path seems to be find all the Natural Number coordinate pairs on the line and stay at .
-
Best guess it the point, (2,7).
The number, ?
No other natural number combination on that line for .

CHECK THIS:
?
yes.
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
27
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A number is between 20 and 30 and is three times the sum of its digits. What is the number?
Let tens and units digits be T and U, respectively
Then number is: 10T + U
So, 20 < 10T + U < 30 ------- inequality (i)
Also, 10T + U = 3(T + U)____10T + U = 3T + 3U___7T = 2U___ ----- inequality (ii)
20 < 10T + < 30 ------ Substituting for U in inequality(i)
40 < 20T + 7T < 60 ----- Multiplying by LCD, 2
40 < 27T < 60
------ Dividing by 27

Since tens digit, or , but , then T or tens digit MUST BE 2
U = 7(2)/2 ------- Substituting 2 for T in inequality (ii)
, or 7
With T being 2 and U being 7, number is:
You can do the check!!
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