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# If Sam were twice as old as he is, he would be 40 years older than Jim

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Joined: 02 Sep 2009
Posts: 50004
If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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17 Sep 2018, 23:13
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Difficulty:

15% (low)

Question Stats:

80% (00:59) correct 20% (01:34) wrong based on 59 sessions

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If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

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If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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Updated on: 18 Sep 2018, 00:19
Bunuel wrote:
If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

2S=40+J -----1
J=S-10 -------2

substituting 2 in 1

2J+20 = 40 + J
J=20
S=30

Originally posted by CounterSniper on 17 Sep 2018, 23:41.
Last edited by CounterSniper on 18 Sep 2018, 00:19, edited 2 times in total.
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Joined: 09 Jul 2018
Posts: 29
If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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Updated on: 18 Sep 2018, 02:41
Bunuel wrote:
If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

Ans is B
Let Sam present age is x
So Jim age=2x-40
Also Jim age= x-10
Therefore x-10=2x-40
x=30

Originally posted by ritu1009 on 17 Sep 2018, 23:53.
Last edited by ritu1009 on 18 Sep 2018, 02:41, edited 1 time in total.
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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18 Sep 2018, 00:11
1
CounterSniper wrote:
Bunuel wrote:
If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

2S=40+J -----1
J-10=S -------2

substituting 2 in 1

2J-20 = 40 + J
J=60
S=50

Hi,
As per the question, Jim is younger than Sam but the highlighted expression implies Sam is 10 years younger than Jim.
It should be $$J = S-10$$.

Same issue with the final values you've calculated as well - Jim's age has turned out to be 10 years more than Sam's
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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23 Sep 2018, 16:38
Bunuel wrote:
If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

We can let the current age of Sam and Jim = S and J, respectively, and create the equations:

2S = J + 40

and

J = S - 10

Substituting, we have:

2S = S - 10 + 40

S = 30

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Joined: 15 Sep 2018
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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27 Sep 2018, 00:57
Let $$x$$ be Sam’s age and let $$y$$be Jim’s age. We can now translate the following phrases into algebraic expressions:

“Twice Sam’s age is 40 years greater than Jim’s age.“

$$2 \times \ Sam’s \ age = Jim’s \ age + 40$$

$$2x = y + 40$$

“Jim’s age is 10 years less than Sam’s age.“
$$Jim’s \ age \ = Sam’s \ age – 10$$
$$y = x – 10$$

We can now solve the system of equations using substitution.

$$2x = y + 40$$

Replace $$y$$ with $$(x – 10)$$:

$$2x =$$ $$(x – 10)$$ $$+ 40$$
$$2x = x + 30$$
$$x = 30$$

Therefore, Sam is 30 years old. The final answer is .
Re: If Sam were twice as old as he is, he would be 40 years older than Jim &nbs [#permalink] 27 Sep 2018, 00:57
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