Solving Linear System Word Problem

Question

For example, if a person wants to earn 250 dollars doing yardwork, and can earn 8 dollars/per hour weeding flower beds and $10/per hour mowing lawn,and wants to work a total of 200 hours, how can you format this to find out how many hours each job must be done? Using the the ax+by=c format.

Answer 1

Let:

• $x$ be the amount of hours weeding flower beds
• $y$ be the amount of hours mowing lawn.

So, the equation system is $$\left\{\begin{array}08x+10y=250\\ x+y=200\end{array}\right.$$

Steps to solve

Multiplying the second equation by $8$ yields $$\left\{\begin{array}08x+10y=250\\ 8x+8y=1600\end{array}\right.$$ Subtracting the second equation from the first yields $$2y=-1350\\ y=-675$$ Substituting that into $x+y=200$ yields $$x+(-675)=200\\ x=200+675\\ x=875$$ Therefore, $x=875$ and $y=-675$.