Question 851625: If Tony’s age + Cherie’s age = 80 and Tony’s age + Gordon’s age = 98 and
Cherie’s age + Gordon’s age = 94, how old are Tony, Cherie and Gordon?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve, we need to set up a few equations. Let's use letters to represent the ages of each person:
t = Tony's age
c = Cherie's age
g = Gordon's age
We are told that Tony's age + Cherie's age is 80. In other words, t + c = 80.
We are told that Tony's age + Gordon's age is 98. So, t + g = 98.
We are told that Cherie's age + Gordon's age is 94. So, c + g = 94
Now we have 3 equations:
t + c = 80
t + g = 98
c + g = 94
If we rewrite the first equation in terms of t, we get t = 80 - c. Now, we can substitute 80 - c for t in our second equation:
80 - c + g = 98
We can rewrite this, so the letters are on one side of the equation and the numbers are on the other side. To do this, we subtract 80 from both sides, giving us:
-c + g = 18
Now, we can add this equation to equation #3:
-c + g + c + g = 94 + 18
Combining like terms gives us:
2g = 112
Dividing both sides by 2 will give us g (Gordon's age):
g = 56
Now that we know Gordon's age, we can replace g with 56 in the second equation:
t + 56 = 98
Subtracting 56 from both sides will give us t (Tony's age):
t = 42
Now that we know Tony's age, we can replace t with 42 in the first equation:
42 + c = 80
Subtracting 42 from both sides will give us Cherie's age:
c = 38
We now have all of the people's ages:
Tony's Age = 42
Cherie's Age = 38
Gordon's Age = 56
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