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Sam got twice as many as Joe, Algebra Word Problem

by Rebecca
(Colorado)










































If there were 109,000 votes and Sam got twice as many as Joe and Mary got 15,000 less than Joe. How many votes did Joe get

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Nov 30, 2011
Algebra - Word Problem - Votes
by: Staff



Question:

by Rebecca
(Colorado)


If there were 109,000 votes and Sam got twice as many as Joe and Mary got 15,000 less than Joe. How many votes did Joe get?


Answer:

Sam’s votes = Sam

Joe’s votes = Joe

Mary’s votes = Mary


Sam + Joe + Mary = 109,000

Sam = 2*Joe

Mary = Joe - 15,000


You have three equations and three unknowns:

Sam + Joe + Mary = 109,000

Sam = 2*Joe

Mary = Joe - 15,000



Solve the equations for Sam, Joe, and Mary using the substitution method.


Solve for Joe


Sam + Joe + Mary = 109,000

Sam = 2*Joe


Substitute 2*Joe for Sam in the 1st equation

2*Joe + Joe + Mary = 109,000


Mary = Joe - 15,000

Substitute Joe - 15,000 for Mary in the 1st equation


2*Joe + Joe + Joe - 15,000 = 109,000


There is now only one equation with one unknown:

2*Joe + Joe + Joe - 15,000 = 109,000



Combine like terms

4*Joe - 15,000 = 109,000


Remove the 15,000 from the left side of the equation by adding 15,000 to each side of the equation.

4*Joe - 15,000 = 109,000

4*Joe - 15,000 + 15,000 = 109,000 + 15,000

4*Joe + 0 = 109,000 + 15,000

4*Joe = 109,000 + 15,000

4*Joe = 124,000


Remove the 4 from the left side of the equation by dividing each side of the equation by 4.

4*Joe = 124,000

4*Joe / 4 = 124,000 / 4

Joe * (4 / 4) = 124,000 / 4

Joe * (1) = 124,000 / 4

Joe = 124,000 / 4

Joe = 31,000 votes


Compute the votes for Sam and Mary

Sam = 2*Joe

Sam = 2*31,000

Sam = 62,000 votes



Mary = Joe - 15,000

Mary = 31,000 - 15,000

Mary = 16,000 votes



The final answer is:

Joe received 31,000 votes

Sam received 62,000 votes

Mary received 16,000 votes




Thanks for writing.

Staff
www.solving-math-problems.com



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