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# Paul has s fewer dollars than Jane has, and together they have a total

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Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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25 Jul 2018, 20:28
00:00

Difficulty:

45% (medium)

Question Stats:

76% (01:10) correct 24% (01:27) wrong based on 39 sessions

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Paul has s fewer dollars than Jane has, and together they have a total of t dollars. Which of the following represents the number of dollars that Paul has?

A. (t – s)/2

B. t/2 – s

C. t – s/2

D. 2s – t

E. s – 2t

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Re: Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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25 Jul 2018, 20:33
Paul and Jane together have t dollars

Let p be the number of dollars Paul has

Paul has s fewer dollars than Jane has = > Jane has (p + s) dollars

=> p + (p + s) = t

=> 2p + s = t

=> 2p = t - s

=> p = $$\frac{(t-s)}{2}$$

Hence option A
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Re: Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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25 Jul 2018, 22:19

Solution

Given:
• Paul has s fewer dollars than Jane has.
• Together, Paula and Jane have t dollars.

To find:
• The option which correctly represents the number of dollar that Paul has

Approach and Working:

• Let paula has ‘r’ dollars.
o Hence, Jane has ‘r+s’ dollars."

• Now, r+r+s= t
o 2r+s=t
o r= $$\frac{(t-s)}{2}$$

Hence, the correct answer is option A.

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Re: Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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25 Jul 2018, 22:26
Bunuel wrote:
Paul has s fewer dollars than Jane has, and together they have a total of t dollars. Which of the following represents the number of dollars that Paul has?

A. (t – s)/2

B. t/2 – s

C. t – s/2

D. 2s – t

E. s – 2t

We can assign variables for the amount paul and jane has.

jane = j

paul = p

j = p + s

Total :

p + p + s = t

2p = t-s

$$p = \frac{(t-s)}{2}$$

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Affiliations: Target Test Prep
Joined: 04 Mar 2011
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Re: Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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30 Jul 2018, 10:31
Bunuel wrote:
Paul has s fewer dollars than Jane has, and together they have a total of t dollars. Which of the following represents the number of dollars that Paul has?

A. (t – s)/2

B. t/2 – s

C. t – s/2

D. 2s – t

E. s – 2t

Letting P and J be equal to the number of dollars owned by Paul and Jane, respectively, we can create the equations:

P + s = J

and

P + J = t

Substituting, we have:

P + P + s = t

2P + s = t

2P = t - s

P = (t - s)/2

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Re: Paul has s fewer dollars than Jane has, and together they have a total  [#permalink]

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30 Jul 2018, 12:49
1
Bunuel wrote:
Paul has s fewer dollars than Jane has, and together they have a total of t dollars. Which of the following represents the number of dollars that Paul has?

A. (t – s)/2

B. t/2 – s

C. t – s/2

D. 2s – t

E. s – 2t

Solve this one by choosing numbers.

Paul has 1 dollar, Jane has 2 dollars. So, s = 2-1 = 1 and t = 2+1 = 3.

Plug s = 1 and t = 3 into the answer choices. The question asks how much money Paul has, so the right answer will give you Paul's amount of money, or 1.

(A) (3-1)/2 = 1 - correct
(B) 3/2 - 1 = 1/2 - wrong
(C) 3 - 1/2 = 5/2 - wrong
(D) 2(1) - 3 = -1 - wrong
(E) 1 - 2(3) = -5 - wrong
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Re: Paul has s fewer dollars than Jane has, and together they have a total &nbs [#permalink] 30 Jul 2018, 12:49
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