Question 975729: I have 3 children. One is the same age as the first number in my age, another if the same age as the second number of my age, and the third is the same age as the sum of the two numbers in my age. None of the children are the same age and the total of our ages is 45
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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
| x | y |
|---|
| 0 | 15 | | 1 | 11 | | 2 | 7 | | 3 | 3 | | 4 | -1 | | 5 | -5 | | 6 | -9 | | 7 | -13 | | 8 | -17 | | 9 | -21 |
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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