How do I solve this problem?

Question

Suppose you have a job mowing lawns that pays $12 per hour. You also have a job at a clothing store that pays $10 per hour. You need to earn at least $350 per week, but you can work no more than 35 hrs per week. You must work a minimum of 10 hrs per week at the clothing store. What is a graph showing how many hours per week you can work at each job?

Answer 1

To solve this problem, you need to set up the equations.

 

First, choose variables.

Let x = number of hours mowing lawns

Let y = number of hours working clothing store

Money from both jobs must be at least $350

(350 or more)

 

12x + 10y ≥ 350

 

Solve for y in order to graph

y ≥ -12/10x +35

 

Minimum of 10 hours at store

y ≥ 10

 

No more than 35 hours a week

x + y ≤ 35

Solve for y to graph

y ≤ -x + 35

 

Making the graph:  Number x and y axis from 0 to 35

 

First equation: y ≥ -12/10x + 35

y-intercept is 35

slope: solid line starting at 35 on the y-axis, go down 12, over 10

Shade above solid line

 

Second equation:

y≥ 10

Make a solid horizontal line at y=10

Shade above line for greater than.

 

Third equation:

y ≤ -x +35

Starting at y-intercept (0,35)

Solid line, Count slope down 1 and over 1

Shade under line

 

The overlapping area on the graph will look like a narrow triangle: above the horizontal line, under the line from the third equation, and above the line of the first equation.

 

The shaded area of the graph represents all the possible combinations of hours for mowing lawns and working the clothing store that meet the requirements based on the pay and time.