Question 975729
x = tenths digit in your age
y = units digit in your age
x and y are positive whole numbers AND they are single digits (0 through 9)


your age = 10x+y
child1's age = x
child2's age = y
child3's age = x+y


sum of the three children's ages = (x)+(y)+(x+y) = 2x+2y


Sum of childrens' ages + parent's age = (2x+2y) + (10x+y) = 12x+3y = 45



12x+3y = 45
4x+y = 15
y = -4x+15


Now make a table for y = -4x+15
Since x is a single digit, this means x is a whole number from 0 to 9

<table border=1><tr><th>x</th><th>y</th></tr><tr><td>0</td><td>15</td></tr><tr><td>1</td><td>11</td></tr><tr><td>2</td><td>7</td></tr><tr><td>3</td><td>3</td></tr><tr><td>4</td><td>-1</td></tr><tr><td>5</td><td>-5</td></tr><tr><td>6</td><td>-9</td></tr><tr><td>7</td><td>-13</td></tr><tr><td>8</td><td>-17</td></tr><tr><td>9</td><td>-21</td></tr></table>


Notice how y is a positive whole number, AND a single digit, when x = 2 or x = 3. The other x values either have y being a double digit number or with y being a negative number. So ignore those other rows.


If x = 2, then y = 7
Parent's age = 27
Child1's age = 2
Child2's age = 7
Child3's age = 2+7 = 9


Sum of ages of parent+children = 27+2+7+9 = 45



If x = 3, then y = 3
Parent's age = 33
Child1's age = 3
Child2's age = 3
Child3's age = 3+3 = 6


Sum of ages of parent+children = 33+3+3+6 = 45


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So your age is either 27 or 33. Either age works. 


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