Mr. Ross's Lawn and Garden Services: A Case of Profit and Equations

Mr. Ross, a local gardener, mows lawns for $8 per lawn and weeds gardens for $10 per garden. One day, he completed a total of 8 jobs and earned a total of $72. The question is, how many of these jobs were lawn mowing and how many were weeding?

Setting up the Equations

To solve this, we can use algebraic equations. Let's denote the number of lawns mowed as x and the number of gardens weeded as y. We know the total number of jobs is 8, and the total earnings are $72.

Therefore, we can set up the following two equations:

Solving the Equations

We can solve these equations using the elimination method. Start by multiplying the first equation by 10 to eliminate the variables:

1   10y  80
8x   10y  72

Subtract the second equation from the first:

1   10y - (8x   10y)  80 - 72
2x  8
x  4

Now that we have the value of x, we can substitute it back into the first equation to find y:

4   y  8
y  4

So, Mr. Ross mowed 4 lawns and weeded 4 gardens.

Alternative Solutions

Another way to solve this is by considering the average earned per job.

Total earnings / Total jobs  Average earnings per job
72 / 8  9

The average rate for mowing lawns and weeding gardens is $9, which means:

Total mowing earnings  4x8  32
Total weeding earnings  4x10  40
32   40  72

This confirms that the answer is 4 lawns and 4 gardens.

Conclusion

Through algebraic equations and logical reasoning, we determined that Mr. Ross mowed 4 lawns and weeded 4 gardens. This solution not only provides a clear answer but also reinforces the understanding of how to solve such problems using different mathematical methods.