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Ben is three times as old as Ron. Ed is 8 years younger than Ben. Ron is 7 years older than Ken. If the sum of the ages of all four people is 161, how many years old is Ron?

Title

Ron's Age

Your Result

Correct

Difficulty

Medium

Your Pace

1:54

Others' Pace

3:00

Video Explanation


Text Explanation

All of the ages are related to each other, so we want to get each person's age in terms of the same variable. That way we can put them all into one equation and solve :) To start, let's focus on Ken. Let x = Ken's age. Ron is 7 years older, so Ron = x+7. Don't forget that we can covert English to math and read that expression directly from the question. "Ron is 7 years older than Ken." Change "is" to "=" and "older than" to "+" and we have Ron = 7 + Ken. We already said that Ken = x, so Ron = x+7. Next we have Ben is three times as old as Ron. That means Ben = 3(x+7). Last we have Ed is 8 years younger than Ben. So, Ed = 3(x+7) – 8. Now we have an expression for each person's age in terms of x. We know that all of the ages add up to 161, so put them all in one equation:

Ken + Ron + Ben + Ed = 161

x + (x+7) + 3(x+7) + 3(x+7) – 8 = 161. 

Combine like terms and we can solve for x. The video explanation matches each expression by color to make it easier to see, and that is reproduced below:

Once we get x=15, we can find Ron's age. Ron is 7 years older than Ken, so Ron = 15+7 = 22.

FAQ: How do we determine Ken is the youngest?

We can't definitively determine that Ken is the youngest from the reading alone. However, we can make an educated guess that Ken is most likely the youngest of the group.

Ben is three times as old as Ron. <-- Ben can't be the youngest. Ed is 8 years younger than Ben. <-- Ed could be the youngest. Ron is 7 years older than Ken. <-- Ron can't be the youngest, but Ken can. 

Since Ron is one-third of Ben's age, and Ken is 7 years younger than Ron, it's safe to say that Ken is younger than Ed, the latter of whom is only 8 years younger than Ben,  it would be sound to think that Ken must be the youngest, because Ken is younger than two people, Ed is only younger than one, and the difference between Ben and Ed's ages and Ron and Ken's ages is about the same.

The truth is, though, that it doesn't matter where you start, because you're just finding the algebraic relationship between the people, which will be the same no matter who you decide is "x". For example we could start with Ron as "x". 

Ron: x 
Ken: x − 7 
Ben: 3x 
Ed: 3x − 8 
Then you'd have: 
x + x − 7 + 3x + 3x − 8 = 161 
8x = 176 
x = 22 
Ron's age is 22.

Related Lessons

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