your club is baking strawberry and apple pies for a bake sale. They need at most 18 pies, and cannot have more than 12 apple pies. Write and graph a system of inequalities to model this system.
Thank you!
You are welcome.
To write and graph a system of inequalities to model this situation, we need to define two variables: let's use "s" to represent the number of strawberry pies and "a" to represent the number of apple pies.
Here are the given conditions:
1. They need at most 18 pies, which means "s + a" should be less than or equal to 18.
Inequality 1: s + a ≤ 18
2. They cannot have more than 12 apple pies, which means "a" should be less than or equal to 12.
Inequality 2: a ≤ 12
Now, let's graph these inequalities.
To graph Inequality 1, we will first graph the equation s + a = 18. This will give us a boundary line:
- Plot two points on the graph representing s=0 and a=18.
- Connect the points with a straight line.
Since the inequality is "s + a ≤ 18," we shade the region below the line.
Next, let's graph Inequality 2. We will graph the equation a = 12, which is a vertical line at a=12 on the x-axis.
Since the inequality is "a ≤ 12," we shade the region to the left of the line.
The shaded region common to both inequalities represents the solution.
The resulting graph should show a shaded triangular region below the line s+a=18, and to the left of the vertical line a=12.
s + a < /= 18
a < 12
call vertical (y) axis s
call horizontal (x) axis a
then
s+a = 18 slopes down at slope = 1 from (0,18) to (18,0)
need to be below or on it
a = 12 is a vertical line at 12
need to be on or to the left of it
so your shaded region is below the slanted line and left of the vertical one