buy bagels and donuts for at least 15 of his students, he only has $48 to spend. Bagels= $3 and donuts= $2. Write and graph a system of linear inequalities.

Question

Write and graph a system of linear inequalities.

Answer 1

Let x = the number of bagels

Let y = the number of donuts

 

x + y ≥ 15 ... this is the inequality for how many of each (eq1) ... We know to use ≥ because "at least" means "no less than" which also means "greater than or equal to."

3x + 2y ≤ 48 ... this is the inequality for how much money is spent (eq2) ... We know to use ≤ because you can't spend more money than you have.

 

I'll re-write these in slope-intercept form so they'll be easier to graph.

EQ1

x + y ≥ 15

y ≥ -x + 15 ... subtract x from both sides

Draw a line crossing the y-axis at 15. The line has a slope of -1.

Shade above the line.

 

EQ2

3x + 2y ≤ 48

2y ≤ -3x + 48 ... subtract 3x from both sides

y ≤ -³/₂x + 16 ... divide both sides by 2

Draw a line that crosses the y-axis at 16. The line has a slope of -³/₂.

Shade below the line.

 

The lines should intersect at (2,13).