Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now ?
What is the best and quickest way to work this out ?
Thanks.
II
Jim is twice as old as Fred ...
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I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?sujaysolanki wrote:Jim 2x
Fred x
Sam x-2
Four years ago
2x - 4 = 4(x-2-4)
x comes to 10
So Jim should be 20
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Thats a good point ! I understood it to be Sam's age 4 years ago.preciousrain7 wrote:I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?sujaysolanki wrote:Jim 2x
Fred x
Sam x-2
Four years ago
2x - 4 = 4(x-2-4)
x comes to 10
So Jim should be 20
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preciousrain7, it should be compared with Sam's age 4 years ago otherwise it will be mentioned in the Qs to compare Jim's age 4yrs ago with Sam's current age!I was wondering if when they "four years ago Jim was 4 times as old as Sam" Are they referring to Sam's Current age or Sam's age 4 years ago?
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
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I've added the answer choices....
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred.
Let x = Fred's age TODAY
So, 2x = Jim's age TODAY
And x - 2 = Sam's age TODAY
AGES FOUR YEARS AGO
Let's first determine Jim's age and Sam's age FOUR YEARS AGO
If 2x = Jim's age TODAY, then 2x - 4 = Jim's age FOUR YEARS AGO
If x - 2 = Sam's age TODAY, then x - 2 - 4 = Sam's age FOUR YEARS AGO
Four years ago Jim was 4 times as old as Sam.
In other words, the value of 2x - 4 is 4 times the value of x - 2 - 4
So, we can write: 2x - 4 = 4(x - 2 -4)
Simplify right side: 2x - 4 = 4(x - 6)
Expand right side: 2x - 4 = 4x - 24
Add 24 to both sides: 2x + 20 = 4x
Subtract 2x from both sides: 20 = 2x
Solve: x = 10
How old is Jim NOW?
2x = Jim's age TODAY
Since x = 10, we know that Jim's age = 2(10) = 20
Answer: D
Cheers,
Brent
TODAY'S AGESII wrote:Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now ?
A. 8
B. 12
C. 16
D. 20
E. 24
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred.
Let x = Fred's age TODAY
So, 2x = Jim's age TODAY
And x - 2 = Sam's age TODAY
AGES FOUR YEARS AGO
Let's first determine Jim's age and Sam's age FOUR YEARS AGO
If 2x = Jim's age TODAY, then 2x - 4 = Jim's age FOUR YEARS AGO
If x - 2 = Sam's age TODAY, then x - 2 - 4 = Sam's age FOUR YEARS AGO
Four years ago Jim was 4 times as old as Sam.
In other words, the value of 2x - 4 is 4 times the value of x - 2 - 4
So, we can write: 2x - 4 = 4(x - 2 -4)
Simplify right side: 2x - 4 = 4(x - 6)
Expand right side: 2x - 4 = 4x - 24
Add 24 to both sides: 2x + 20 = 4x
Subtract 2x from both sides: 20 = 2x
Solve: x = 10
How old is Jim NOW?
2x = Jim's age TODAY
Since x = 10, we know that Jim's age = 2(10) = 20
Answer: D
Cheers,
Brent
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We can let J, S, and F = the current age of Jim, Fred, and Sam, respectively, and create the equations:II wrote:Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now ?
What is the best and quickest way to work this out ?
Thanks.
II
J = 2F
and
S = F - 2
S + 2 = F
and
J - 4 = 4(S - 4)
J - 4 = 4S - 16
J = 4S - 12
Since J = 2F we have:
2F = 4S - 12
F = 2S - 6
Since S + 2 = F, we have:
S + 2 = 2S - 6
8 = S
So J = 4 x 8 - 12 = 20.
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