SOLUTION: John is 7 times older than Sally in 10 years their combined age will be 71. How old is John

Question 618965: John is 7 times older than Sally in 10 years their combined age will be 71. How old is John
Found 2 solutions by josmiceli, lenny460:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = John's age now
Let = Sally's age now
= John's age in 10 years
= Sally's age in 10 years
given:
(1)
(2)
----------------------
(2)
(2)
Substitute (1) into (2)
(2)
(2)
(2)
and
(1)
(1)
Note that
John is 44 years and 7 and 1/2 months old
check answer:
(2)
(2)
(2)
and
(1)
(1)
(1)
OK
Answer by lenny460(1073) (Show Source): You can put this solution on YOUR website!
Let the age of John be: 7n
Let the age of Sally be: n
So the ages of John and Sally is: 7n + n
In 10 years their ages will be:
John 7n + 10
Sally n + 10
Therefore:
7n + 10 + n + 10 = 71
Combine like terms:
7n + n = 8n
10 + 10 = 20
8n + 20 = 71
Subtract 20 from each side of the equation:
8n + 20 - 20 = 71 - 20
20 - 20 = 0
71 - 20 = 51
Therefore:
8n = 51
Divide each side by 8
8n/8 = 51/8
n = 6 years 4 1/2 months
Sally is 6 years 4 1/2 months
John's age is: 7n
Therefore:
7(6years 4 1/2 months)
7 * 6 = 42 years
7 * 4 1/2 = 31 1/2 months
31 1/2 months = 2 years 7 1/2 months
John"s age:
42 years + 2 years 7 1/2 months = 44 years 7 1/2 months
Sally is 6 years 4 1/2 months
John is 44 years 7 1/2 months
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