Answer:
Answer in explanation
Explanation:
Linear Modeling
It's given a situation where a student has two summer jobs and wants to collect $750 to pay for a down payment on a car. He gets paid $25 for each lawn mowed and $15 for each pool cleaned
- Create a model in standard form
Let
x = number of lawns mowed
y = number of pools cleaned
He wants to make $750, thus:
25x + 15 y = 750
Dividing by 5, we have the model that represents the linear relationship:
5x + 3y = 150
The x-intercept can be found by setting y=0:
5x + 3(0) = 150
5x = 150
Dividing by 5:
x = 150/5 = 30
x = 30
This represents the situation where the student gets his $750 by only mowing 30 lawns, no pools cleaned.
The y-intercept can be found by setting x =0:
5(0) + 3y = 150
3y = 150
y = 150/3 = 50
y = 50
This represents the situation where the student gets his $750 by only cleaning 50 pools, no lawns mowed.
- Identify two combinations that are solutions to the equation
Starting from the basic equation
5x + 3y = 150
We can give x some arbitrary value (less than 30) and find the value for y.
For example, for x=12
5*12 + 3y = 150
60 + 3y = 150
3y = 150 - 60 = 90
y = 90/3=30
This solution corresponds to the case where the student gets $750 by mowing 12 lawns and cleaning 30 pools.
For example, for x=21
5*21 + 3y = 150
105 + 3y = 150
3y = 150 - 105 = 45
y = 45/3=15
This solution corresponds to the case where the student gets $750 by mowing 21 lawns and cleaning 15 pools.