Linear Equation

Question

Write an equation that represents this problem, explain what each part means and why you wrote it that way, and then solve for how many lawns he must mow to make 200 dollars. My son wants to earn money for a bike. He can mow 1 lawn for 18 dollars but it costs him 3 dollars for fuel for the lawn mower. How many lawns will he have to mow to make 200 dollars?

Answer 1

I think I can answer this question! Let x be the number of lawns your son mows, and let y be the number of times he fuels the mower.

If he is paid $18 for every lawn he mows, and pays $3 for every time the mower needs fuel, and the goal is $200, then your equation should look like this:

18x - 3y = 200

This is our linear equation in standard form. To solve for x, the number of lawns your son needs to mow to reach his goal, we must isolate x. First, add 3y to both sides of the equation.

18x = 200 + 3y

Then, divide both sides by 18.

x = (200 + 3y) / 18

As you can see, x depends on the value of y, the number of times he needs to fuel his mower, which we are not given. It is worth noting, however, that 18 is 6 times the value of 3. At this point, you could plug in some test values to see what gives you exactly 200.

For instance, if your son mowed 14 lawns, that would earn him $252, because 18 • 14 = 252. If he had to fuel his mower after every single time he used it, 14 times, it would cost him $42, since 14 • 3 = 42.

252 - 42 = 210

If your son mowed 14 lawns, he would meet his goal of $200 with $10 to spare.

However, if your son mowed 13 lawns, he would earn $234, but if he fueled 13 times, it would cost him $39.

234 - 39 = 195

That is not enough.

Since we can't multiply by whole numbers to get exactly 200, an inequality may be more appropriate here.

18x - 3y ≥ 200

x ≥ (200 + 3y) / 18

Hope this helps!

Answer 2

Net profit per job = 18-3 = 15

200/15 = 13⁺, i.e. he will need to mow 14 lawns.