Transcript Leyla is selling hot dogs and spicy sausages at the fair.
Slide 1
Leyla is selling hot dogs and spicy sausages at
the fair. She has only 40 buns, so she can sell
no more than a total of 40 hot dogs and spicy
sausages. Each hot dog sells for $2, and each
sausage sells for $2.50. Leyla needs at least
$90 in sales to meet her goal. Write and graph
a system of inequalities that models this
situation.
Slide 2
Let d represent the number of hot dogs, and let s
represent the number of sausages.
The total number of buns Leyla has can be modeled
by the inequality d + s ≤ 40.
The amount of money that Leyla needs to meet
her goal can be modeled by 2d + 2.5s ≥ 90.
The system of inequalities is
d0
s0
d + s ≤ 40
2d + 2.5s ≥ 90
.
Slide 3
Graph the solid boundary
line d + s = 40, and shade
below it.
Graph the solid boundary
line 2d + 2.5s ≥ 90, and
shade above it. The
overlapping region is the
solution region.
Slide 4
Check Test the point (5, 32) in both inequalities.
This point represents selling 5 hot dogs and 32
sausages.
d + s ≤ 40
2d + 2.5s ≥ 90
5 + 32 ≤ 40
37 ≤ 40
2(5) + 2.5(32) ≥ 90
90 ≥ 90
Slide 5
Graphing Systems of Inequalities
Graph the system of inequalities.
y<
–3
y ≥ –x + 2
For y < – 3, graph the
dashed boundary line
y = – 3, and shade below
it.
For y ≥ –x + 2, graph the
solid boundary line
y = –x + 2, and shade above it.
The overlapping region is the solution region.
Slide 6
Helpful Hint
If you are unsure which direction to shade, use
the origin as a test point.
Slide 7
Systems of inequalities may contain more
than two inequalities.
Slide 8
Graph the system of inequalities, and classify
the figure created by the solution region.
x ≥ –2
x≤3
y ≥ –x + 1
y≤4
Slide 9
Graph the solid boundary
line x = –2 and shade to the
right of it. Graph the solid
boundary line x = 3, and
shade to the left of it.
Graph the solid boundary
line y = –x + 1, and shade
above it. Graph the solid
boundary line y = 4, and
shade below it. The
overlapping region is the
solution region.
Slide 10
Graph the system of inequalities, and classify
the figure created by the solution region.
x≤6
y≤
x+1
y ≥ –2x + 4
Slide 11
Graph the solid boundary
line x = 6 and shade to the
left of it.
Graph the solid boundary
line, y ≤ x + 1 and shade
below it.
Graph the solid boundary
line y ≥ –2x + 4, and shade
below it.
The overlapping region is
the solution region. The
solution is a triangle.
Leyla is selling hot dogs and spicy sausages at
the fair. She has only 40 buns, so she can sell
no more than a total of 40 hot dogs and spicy
sausages. Each hot dog sells for $2, and each
sausage sells for $2.50. Leyla needs at least
$90 in sales to meet her goal. Write and graph
a system of inequalities that models this
situation.
Slide 2
Let d represent the number of hot dogs, and let s
represent the number of sausages.
The total number of buns Leyla has can be modeled
by the inequality d + s ≤ 40.
The amount of money that Leyla needs to meet
her goal can be modeled by 2d + 2.5s ≥ 90.
The system of inequalities is
d0
s0
d + s ≤ 40
2d + 2.5s ≥ 90
.
Slide 3
Graph the solid boundary
line d + s = 40, and shade
below it.
Graph the solid boundary
line 2d + 2.5s ≥ 90, and
shade above it. The
overlapping region is the
solution region.
Slide 4
Check Test the point (5, 32) in both inequalities.
This point represents selling 5 hot dogs and 32
sausages.
d + s ≤ 40
2d + 2.5s ≥ 90
5 + 32 ≤ 40
37 ≤ 40
2(5) + 2.5(32) ≥ 90
90 ≥ 90
Slide 5
Graphing Systems of Inequalities
Graph the system of inequalities.
y<
–3
y ≥ –x + 2
For y < – 3, graph the
dashed boundary line
y = – 3, and shade below
it.
For y ≥ –x + 2, graph the
solid boundary line
y = –x + 2, and shade above it.
The overlapping region is the solution region.
Slide 6
Helpful Hint
If you are unsure which direction to shade, use
the origin as a test point.
Slide 7
Systems of inequalities may contain more
than two inequalities.
Slide 8
Graph the system of inequalities, and classify
the figure created by the solution region.
x ≥ –2
x≤3
y ≥ –x + 1
y≤4
Slide 9
Graph the solid boundary
line x = –2 and shade to the
right of it. Graph the solid
boundary line x = 3, and
shade to the left of it.
Graph the solid boundary
line y = –x + 1, and shade
above it. Graph the solid
boundary line y = 4, and
shade below it. The
overlapping region is the
solution region.
Slide 10
Graph the system of inequalities, and classify
the figure created by the solution region.
x≤6
y≤
x+1
y ≥ –2x + 4
Slide 11
Graph the solid boundary
line x = 6 and shade to the
left of it.
Graph the solid boundary
line, y ≤ x + 1 and shade
below it.
Graph the solid boundary
line y ≥ –2x + 4, and shade
below it.
The overlapping region is
the solution region. The
solution is a triangle.