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

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Bunuel
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Paul has s fewer dollars than Jane has, and together they have a total [#permalink] New post   25 Jul 2018, 21:28
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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] New post   30 Jul 2018, 13:49
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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 [#permalink] New post   25 Jul 2018, 21:33
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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] New post   25 Jul 2018, 23:19
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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.

Answer: A
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Re: Paul has s fewer dollars than Jane has, and together they have a total [#permalink] New post   25 Jul 2018, 23:26
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

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

The best answer is A.
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Re: Paul has s fewer dollars than Jane has, and together they have a total [#permalink] New post   30 Jul 2018, 11:31
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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

Answer: A
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Re: Paul has s fewer dollars than Jane has, and together they have a total [#permalink]
30 Jul 2018, 11:31
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