Chapter 8 linear appliCaTionS 249EXAMPLE
Jill is twice as old as Jim and Jim is 3 years older than Ken. The sum of their
ages is 61. What are their ages?
Three quantities are being compared, so we find one age and relate the
other two ages to it. This allows us to represent the sum using only one
variable. Ken’s age is being compared to Jim’s and Jim’s to Jill’s. One route
to take is to let x represent Jim’s age. We can then write Jill’s age in terms of
Jim’s age: 2x. Jim is 3 years older than Ken, so Ken is 3 years younger than
Jim. This makes Ken’s age as x – 3. The sum of their ages is 61.
xxx
xx
x
x++−=
−=
++
=
=
=2361
4361
33
464
64
4
16()Jim’s age is 16; Jill’s age is 2x = 2(16) = 32; and Ken’s age is x − 3 = 16 − 3 = 13.
Karen is 4 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 we 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^12 x.
xx xx xx xx+ ++=++=
++
=()()(4
24424
24422 4
224422 ))(++)
=
++=
+=
−−
=
=24 2
288
48 88
5888
88
580xxx
xx
x^880
5
x= 16Robert’s age is 16; Karen’s age is x + 4 = 16 + 4 = 20; and Jerri’s,^12 x (= ^1216 ) = ^8.
EXAMPLE
Jill is twice as old as Jim and Jim is 3 years older than Ken. The sum of their