Age Problems
Algebra students are often asked to compute people’s ages. The steps in solving such problems are usually the same as those used above.
Examples
Example 1:
Jill is twice as old as Jim and Jim is three years older than Ken. The sum of their ages is 61. What are their ages?
Three quantities are being compared, so find one age and relate the other two ages to it. Ken’s age is being compared to Jim’s and Jim’s to Jill’s. The easiest route to take is to let x represent Jim’s age. We can write Jill’s age in terms of Jim’s age; 2 x . Jim is three years older than Ken, so Ken is three years younger than Jim. This makes Ken’s age as x – 3.
Jim’s age is 16. Jill’s age is 2 x = 2(16) = 32. Ken’s age is x – 3 = 16 – 3 = 13.
Example 2:
Karen is four years older than Robert, and Jerri is half as old as Robert. The sum of their ages is 44. Find Karen’s, Robert’s, and Jerri’s ages.
Both Karen’s and Jerri’s ages are being compared to Robert’s age, so let x represent Robert’s age. Karen is four years older than Robert, so Karen’s age is x + 4. Jerri is half as old as Robert, so Jerri’s age is .
Robert’s age is 16; Karen’s age is x + 4 = 16 + 4 = 20; and Jerri’s,
Word Problems About Age Practice Problems
Practice
 Andy is three years older than Bea and Bea is five years younger than Rose. If Rose is 28, how old are Andy and Bea?
 Michele is four years younger than Steve and three times older than Sean. If the sum of their ages is 74, how old are they?
 Monica earns three times per hour as John. John earns $2 more per hour than Alicia. Together they earn $43 per hour. How much is each one’s hourly wage?
Solutions
 Because Rose is 28 and Bea is five years younger than Rose, Bea is 28 – 5 = 23 years old. Andy is three years older than Bea, so Andy is 23 + 3 = 26 years old.

Let x = Michele’s age. Steve is four years older, so his age is x + 4. Sean is onethird Michele’s age, so his age is
Michele is 30 years old; Steve is x + 4 = 34; and Sean is
You can avoid the fraction in this problem if you let x represent Sean’s age. Then Michele’s age would be 3 x ; and Steve’s, 3 x + 4.
 Monica’s earnings are being compared to John’s, and John’s to Alicia’s. The easiest thing to do is to let x represent Alicia’s hourly wage. Then John’s hourly wage would be x + 2. Monica earns three times as much as John, so her hourly wage is 3( x + 2).
Alicia earns $7 per hour; John, x + 2 = 7 + 2 = $9; and Monica 3( x + 2) = 3(7 + 2) =$27.
Practice problems for this concept can be found at: Algebra Word Problems Practice Test.
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