The lee's have three children. the oldest is twice as old as the youngest. the middle child is five years older than the youngest. if the sum of the ages is 57, how old is each child?

What do we know about this problem? What do we want to find? We haven't been given any direct numbers, but we have been given some relationships between them. Both the second and the third sentences here refer to the age of the youngest sibling. This seems important - let's call that age y, for "youngest." We'll call the age of the middle child m for "middle" and the age of the oldest o. The last sentence tells us that these all add up to 57, which, using our new labels, gives us the mathematical statement



This is a good start, but we can't really do anything with it yet. Let's try to get everything in terms of one label. What information can we use to get us there?

"The oldest is twice as old as the youngest." This statement relates the oldest's age o to the youngest's age y. Mathematically, it says that , or  if we wanna write a little more efficiently.

"The middle child is five years older than the youngest." Straightforward enough; if we take the youngest's age y and add 5 years, we get the middle's age m. Mathematically, .

Now, let's go back to our sum. Now, we can put everything in terms of y.

becomes . After a little housekeeping, we get:



And solving for y, we arrive at:



The youngest sibling is 13 years old. With that information, we can easily find that the middle sibling is 13 + 5 = 18 years old, and the oldest sibling is 2 x 13 = 26 years old.