Question

The profit on the sale of a bicycle at a bike shop is $30, while the profit on the sale of a tricycle is $20. The owner is interested in making more than $200 in profit per day, and expects to sell at most 9 items per day. The system that represents this situation is

b+4≤9
b+4≤9
and
30b+20t>200
30b+20t>200
. The graph of the boundary lines is shown below. Which region should be shaded (to form the solution)?

Answer 1

Two equations are given

b+t <=9

30b + 20t > 200

WE graph each inequality

b + t <= 9

Make a table for b + t < = 9

b --- > t

0 --> 9

2 --> 7

Plot the point and make a graph. WE shade the bottom region because we have <= symbol

The graph is attached below.

WE graph the inequality

30b + 20t > 200

Make a table for 30b + 20t > 200

b --- > t

0 --> 10

6 --> 1

Plot the point and make a graph. WE shade the upper region because we have > symbol

The intersection of shaded region is our solution.