The smaller number is 4 and the larger is 11 – x == 11 – 4 = 7.
Algebra students are often asked to compute people’s ages. The steps I solving such problems are usually the same as those used above.
Examples
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: 2x. 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 2x = 2(16) = 32. Ken’s age is x – 3 = 16 – 3 = 13.
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 hal as old as Robert, so Jerri’s
age is ½ x.
Robert’s age
is 16; Karen’s age is x + 4 = 16 + 4 = 20, and Jerri’s, ½ x = ½ (16) = 8.
Practice
1. 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?
2. 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?
3. 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
1. 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.
2. Let
x = Michele’s age. Steve is four years older, so his age is x + 4.
Sean
is one-third 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 3x; and Steve’s, 3x + 4.
3. 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) ¼= $27.
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