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“D” dollars is split 3 ways










































   • “D” dollars is split 3 ways

           Scott gets half of what Mary gets

           Alice get three fourths of what Scott gets

   • How much does Scott get?

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Sep 21, 2012
Dividing “D” dollars
by: Staff


Answer:

Part I


You forgot to list how many dollars was to be split three ways in the problem statement..

Because of this omission, I have used the variable “D” to represent the number of dollars involved.

To find the answer in actual dollars, substitute the value of the money which is to be split for the variable “D” in the final answer.


Definitions:

         Scott = the number of dollars Scott receives

         Mary = the number of dollars Mary receives

         Alice = the number of dollars Alice receives


Solution:


         Scott gets half of what Mary gets

                 Scott = ½ * Mary

             Solve for the variable “Mary”

             Multiply each side of the equation by 2

                 2 * Scott = 2 * ½ * Mary

                 2 * Scott = (2 / 2) * Mary

                 2 * Scott = (1) * Mary

                 2 * Scott = Mary

                 Mary = 2*Scott


         Alice gets three fourths of what Scott gets


                 Alice = ¾ * Scott


         The total number of dollars is the sum of the number of dollars each person receives.



                 Scott + Mary + Alice = D

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Sep 21, 2012
Dividing “D” dollars
by: Staff


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Part II


             Substitute 2*Scott for the variable Mary

                 Scott + 2*Scott + Alice = D


             Substitute ¾ * Scott for the variable Alice

                 Scott + 2*Scott + ¾ * Scott = D


             Combine like terms


                 Scott + 2*Scott + ¾ * Scott = D

                 3.75 * Scott = D


             Divide each side of the equation by 3.75

                 3.75 * Scott / 3.75 = D / 3.75

                 Scott * (3.75 / 3.75) = D / 3.75

                 Scott * (1) = D / 3.75

                 Scott = D / 3.75

                 Scott = D / (3 ¾)

                 Scott = D / (15 / 4)

                 Scott = (4/15) * D



             Solve for Mary

                 Mary = 2 * Scott

                 Mary = 2 * (4 / 15) * D

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Sep 21, 2012
Dividing “D” dollars
by: Staff


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Part III

                 Mary = (8/15) * D


             Solve for Alice

                 Alice = ¾ * Scott

                 Alice = ¾ * (4 / 15) * D

                 Alice = (4 / 4) * (3 / 15) * D

                 Alice = (1) * (3 / 15) * D

                 Alice = (3/15) * D

                 Alice = (1/5) * D





Final Answer:

             How much does Scott get?

                 Scott = (4 / 15) * D


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Check the answer:

             Scott + Mary + Alice = D

             (4 / 15) * D + (8/15) * D + (3 / 15) * D = D

             [(4 + 8 + 3) / 15] * D = D

             (15 / 15) * D = D

             1 * D = D

             D = D, OK → Scott = (4 / 15)*D is a valid solution


Thanks for writing.

Staff
www.solving-math-problems.com



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