Help with solving system of equations

This is on the study guide for my final exam. I've spent over half an hour trying to get this problem solved and yet I still find myself stumped. Here's the problem:

Bobby gets $20 dollars for each lawn he mows and $25 for each driveway he shovels. At the end of an unspecified time period, he gets a total of $1,500 and has done a total of 68 jobs.

How many lawns and driveways did he end up doing?

Oh, and a minor side note: I'm very busy and stressed at this moment in time, so (please don't take any offense by this) just guide me through the equation without doing anything that requires me to respond. I noticed this on the last thread I posted on.

Re: Help with solving system of equations

Quote:

Originally Posted by

**Matt93** This is on the study guide for my final exam. I've spent over half an hour trying to get this problem solved and yet I still find myself stumped. Here's the problem:

Bobby gets $20 dollars for each lawn he mows and $25 for each driveway he shovels. At the end of an unspecified time period, he gets a total of $1,500 and has done a total of 68 jobs.

How many lawns and driveways did he end up doing?

Oh, and a minor side note: I'm very busy and stressed at this moment in time, so (please don't take any offense by this) just guide me through the equation without doing anything that requires me to respond. I noticed this on the last thread I posted on.

Let $\displaystyle l$ be the number of lawns he mows and $\displaystyle d$ the amount of driveways he shovels.

As he has done a total of 68 jobs this means that $\displaystyle l + d= 68$ (ie: the total number of jobs is the sum of the number of lawns and driveways)

He gets $\displaystyle 20l$ for mowing the lawns and $\displaystyle 25d$ for the driveways. In total this is 1500: $\displaystyle 20l + 25d = 1500 \Leftrightarrow 4l + 5d = 300$

This means you have two equations and two unknowns so you can use your favourite method of solving simultaneous equations to solve

$\displaystyle l+d = 68 \text{ [eq1]}$

$\displaystyle 4l+5d = 300 \text{ [eq2]}$

Re: Help with solving system of equations

Quote:

Originally Posted by

**Matt93** Oh, and a minor side note: I'm very busy and stressed at this moment in time, so (please don't take any offense by this) just guide me through the equation without doing anything that requires me to respond. I noticed this on the last thread I posted on.

This statement goes completely against the philosophy of the MHF. See forum rule # 11. I'm not "taking offense" at your statement, but I am putting you on notice that your attitude is not in the spirit of MHF. MHF is not a homework service, nor is it a tutorial. The main idea is for posters to show their work, and exactly where they're stuck. Then helpers on MHF get them unstuck by a small hint, at which point the poster continues, etc.