SOLUTION: I'm confused as to how to set this up using two linear equations with two unknowns. "A developer built twice as many three-bedroom homes as four-bedroom homes in a new development

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I'm confused as to how to set this up using two linear equations with two unknowns. "A developer built twice as many three-bedroom homes as four-bedroom homes in a new development      Log On


   

Question 1003684: I'm confused as to how to set this up using two linear equations with two unknowns. "A developer built twice as many three-bedroom homes as four-bedroom homes in a new development. The profit from each three-bedroom home was $25000, and the profit from each four-bedroom home was $35000. If the total profit was $6 800 000, how many of each were built?"
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Very common application for simple two-variable linear system.

Assign variables.
x, how many three-bedroom homes
y, how many four-bedroom homes

Form equations.
system%28x%2Fy=2%2C25000x%2B35000y=6800000%29

If you can understand that, then simply solving the system should be no trouble.

Just watch for simplification mistakes in the money equation.
%2825000x%2B35000y%29%2F%285%2A1000%29=6800000%2F%285%2A1000%29

5x%2B7y=1360
for the equivalent system
system%28x=2y%2C5x%2B7y=1360%29


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The simpler equation shown first is from, ...built twice as many three-bedroom homes as four-bedroom homes in a new development.. This means that x is two times y, or the ratio of x and y is 2.