Question 1026436: the sum of the ages of John and Carl is 72 years. in 12 years time John, the elder person,will be six times as old as what Carl was 21 years ago.
question:
1. what are their current ages?
2. what was the difference between their ages 15 years ago?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let j = john's age today.
let c = carl's age today.
the sum of their ages is 72.
this leads to j + c = 72
in 12 years john will be j + 12 years old.
carl is c years old today.
21 years ago, carl was c - 21 years old.
in 12 years, john will be 6 times as old as carl was 21 years ago leads to:
j + 12 = 6 * (c - 21)
you have 2 equations that need to be solved simultaneously.
they are:
j + c = 72
j + 12 = 6 * (c-21)
there are different ways to solve equations simultaneously.
we'll use elimination this time.
take the second equation and simplify it to get:
j + 12 = 6 * (c-21) becomes j + 12 = 6c - 126
subtract 6c from both sides of the equation and subtract 12 from both sides of the equation to get j - 6c = -12 - 126.
simplify to get j - 6c = -138.
your two equation are now:
j + c = 72
j - 6c = -138
multiply both sides of the second equation by -1 and leave the first equation as is to get:
j + c = 72
-j + 6c = 138
add the equations together to get:
0 + 7c = 210
simplify to get 7c = 210
divide both sides of the equation by 7 to get c = 210 / 7 = 30.
c is equal to carl's age today.
in the equation of j + c = 72, replace c with 30 to get j + 30 = 72.
solve for j to get j = 42.
you have:
john's age = 42 today.
carl's age = 30 today.
in 12 years, john will be 42 + 12 = 54.
21 years ago, carl was 30 - 21 = 9.
in 12 years john is 6 times carl's age 21 years ago.
you get 54 = 6 * 9 = 54.
this confirms the statement is true.
the sum of their ages is 72 (42 + 30).
in 12 years, john is 6 times as old as carl was 21 years ago.
54 = 6 * 9 = 54.
solution looks good.
their current ages are john is 42 and carl is 30.
the second questions is what was the difference between their ages 15 years ago.
15 years ago, john would have been 42 - 15 = 27.
15 years ago, craig would have been 30 - 15 = 15.
the difference in their ages 15 years ago would have been 27 - 15 = 12.
this is natural, since the difference in their ages will always be 12, no matter what age they are.
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