SOLUTION: Alice, Bob, and Mary completed a project and were paid $25,000. Before the project started, they agreed that Alice should be paid $1000 less than twice Mary’s share and Bob shoul

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Alice, Bob, and Mary completed a project and were paid $25,000. Before the project started, they agreed that Alice should be paid $1000 less than twice Mary’s share and Bob shoul      Log On


   

Question 1152295: Alice, Bob, and Mary completed a project and were paid $25,000. Before the project started, they agreed that Alice should be paid $1000 less than twice Mary’s share and Bob should be paid $2000 more than Mary’s share. How much did each earn?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52895) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x = Mary' share.


Then the Alice' share is (2x-1000) dollars,  

and Bob' share is (x+2000).


The equation for the total then is


    x + (2x-1000) + (x+200) = 25000  dollars.


Simplify and solve for x


    4x + 1000 = 25000

    4x = 25000 - 1000 = 24000

     x                = 24000/4 = 6000  dollars.


ANSWER.  Mary' share is $6000;  Alice' share is 2*6000-1000 = 11000 dollars;  Bob' share is  6000+2000 = 8000 dollars.


CHECK.  6000 + 11000 + 8000 = 25000.   ! Precisely correct !

Solved.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a = alice's share
b = bob's share
m = mary's share

a + b + m = 25000

their agreement was:
a = 2 * m - 1000
b = m + 2000

replace a and b with their equivalents to get:
a + b + m = 25000 becomes:
2 * m - 1000 + m + 2000 + m = 25000
combine like terms to get:
4 * m + 1000 = 25000
subtract 1000 from both sides of the equation to get:
4 * m = 24000
solve for m to get:
m = 24000 / 4 = 6000

a = 2 * m - 1000 becomes a = 2 * 6000 - 1000 which becomes a = 11000
b = m + 2000 becomes b = 6000 + 2000 which becomes b = 8000

you have:
a = 11000
b = 8000
m = 6000
a + b + m = 11000 + 8000 + 6000 = 25000

your solution is that:
alice earned 11000
bob earned 8000
mary earned 6000