SOLUTION: Gary is X years old today. Two years ago, his grandfather was three times older than Gary at that time. A The age difference of Gary and his grandfather then was 48 years write a l

Question 1148599: Gary is X years old today. Two years ago, his grandfather was three times older than Gary at that time. A The age difference of Gary and his grandfather then was 48 years write a linear equation to represent this age difference. B find Gary's grandfather's age today
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement, simplify
:
Gary is X years old today.
Let x = Gary's present age
Let g = grandfathers age
Two years ago, his grandfather was three times older than Gary at that time.
g - 2 = 3(x - 2)
g - 2 = 3x - 6
g = 3x - 6 + 2
g = 3x - 4
A The age difference of Gary and his grandfather then was 48 years
write a linear equation to represent this age difference.
g - x = 48
x = g - 48
B find Gary's grandfather's age today
replace x with (g-48) in the first simplified equation
g = 3(g-48) - 4
g = 3g - 144 - 4
g - 3g = -148
g = -148/-2
g = +74 yrs is grandfather's age
:
:
Check this out. Gary's age 74 - 48 = 26
"Two years ago, his grandfather was three times older than Gary at that time."
74 - 2 = 3(26 - 2)
72 = 3(24)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution by the other tutor is quite likely the expected answer.

However, the wording of the question is probably incorrect. With the correct interpretation of the given information, we get a different answer.

In everyday use, "3 times OLDER THAN" is (carelessly) used to mean the same thing as "3 times AS OLD AS". However, grammatically the two are different.

"3 times AS OLD AS x" clearly means "3x".
"3 times OLDER THAN x" means x, plus 3 more times x, which is 4x.

So, with the grammatically correct interpretation of the given information, we have...

x = Gary's age now
x-2 = Gary's age 2 years ago
4(x-2) = his grandfather's age 2 years ago

The difference in their ages (always, including 2 years ago) is 48 years:

Gary is 18; his grandfather is 18+48 = 66.

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