Jeff wants to start a lawn maintenance service to earn money for college. He wants to charge $25 for a small lawn and $35 for a large one. It takes him an average of 2 hours to mow and trim a small lawn and 3 hours to do a large one. He wants to make at least $250 a week but can work no more than 20 hours every week.
If x is the number of small lawns and y is the number of large lawns, which ordered pair is a solution to the system of inequalities which describes Jeff's situation?
Don't see any choices, but we do know
2x + 3y <= 20
25x + 35y >= 250
If he does 10 small lawns, that's 20 hrs and $250
He can't do any large lawns, since he can do at most 8 small lawns for $200, and can't make up the difference and stay under 20 hours:
S L Hrs $$$
10 0 20 250
9 0 18 225
8 1 19 235
7 2 20 245
6 2 18 220
. . .
To determine which ordered pair is a solution to the system of inequalities that describes Jeff's situation, let's break down the problem into equations and inequalities.
Let x represent the number of small lawns Jeff mows and y represent the number of large lawns he mows.
Since it takes 2 hours to mow and trim a small lawn, the total time spent on small lawns will be 2x hours.
Similarly, it takes 3 hours to mow and trim a large lawn, so the total time spent on large lawns will be 3y hours.
Given the constraints:
- Jeff can work no more than 20 hours every week (x + y ≤ 20).
- Jeff wants to make at least $250 (25x + 35y ≥ 250).
Now, let's solve for the ordered pair that satisfies both inequalities.
1. x + y ≤ 20
This inequality represents the constraint that Jeff can work no more than 20 hours. Since this is an inequality, there are several possible ordered pairs that satisfy this condition. Let's choose one of them, for example:
- Let x = 10 (the number of small lawns Jeff mows) and y = 10 (the number of large lawns Jeff mows).
2. 25x + 35y ≥ 250
This inequality represents the constraint that Jeff wants to make at least $250. Let's substitute our chosen values for x and y into the equation and see if it satisfies the condition:
- 25(10) + 35(10) ≥ 250
- 250 + 350 ≥ 250
- 600 ≥ 250
Since 600 is indeed greater than or equal to 250, the chosen ordered pair (x = 10, y = 10) satisfies the condition, and it is a solution to the system of inequalities.
Therefore, the ordered pair (10, 10) is a solution to the system of inequalities which describes Jeff's situation.
To find the ordered pair that is a solution to the system of inequalities, let's first set up the inequalities based on the information given:
Let's say x is the number of small lawns and y is the number of large lawns.
We know that Jeff charges $25 for a small lawn and $35 for a large one. So the amount of money Jeff earns from small lawns, in dollars, would be 25x, and the amount earned from large lawns would be 35y.
We also know that it takes him an average of 2 hours to mow and trim a small lawn and 3 hours to do a large one. So the total time spent on small lawns, in hours, would be 2x, and the total time spent on large lawns would be 3y.
Now let's set up the inequalities:
1. Jeff wants to make at least $250 a week, so the first inequality is:
25x + 35y ≥ 250
2. Jeff can work no more than 20 hours every week, so the second inequality is:
2x + 3y ≤ 20
We now have the system of inequalities:
25x + 35y ≥ 250
2x + 3y ≤ 20
To find the ordered pair that is a solution to this system, we need to find the values of x and y that satisfy both inequalities. One way to do this is by graphing the system of inequalities on a coordinate plane.
Once the graph is plotted, the solution will be the area where the shaded regions of both inequalities overlap. The ordered pairs within this region will represent the combinations of small and large lawns that Jeff can do to satisfy both conditions.
It is not possible to provide a specific ordered pair without further information or a graph to refer to. However, you can use the graph or solve the system algebraically to find the specific ordered pair(s) that represent solutions to Jeff's situation.