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Algebra 2
Write and solve systems of linear inequalities algebraically: word problems
Elena is designing a paint can with thickness
t
t
t
millimeters and height
h
h
h
centimeters. She calculates that the thickness of the can in millimeters must be at least
0
0
0
.
1
1
1
times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used,
(
0.2
+
t
+
0.5
h
)
(0.2+t+0.5 h)
(
0.2
+
t
+
0.5
h
)
cents, must be at most
12
12
12
.
2
2
2
cents. Which of the following systems of inequalities best models the relationship between height and thickness described?
\newline
Choose
1
1
1
answer:
\newline
(A)
{
t
≤
12
−
h
2
10
t
≥
h
\left\{\begin{array}{l}t \leq 12-\frac{h}{2} \\ 10 t \geq h\end{array}\right.
{
t
≤
12
−
2
h
10
t
≥
h
\newline
(B)
{
t
≤
12
−
h
2
t
≥
10
h
\left\{\begin{array}{l}t \leq 12-\frac{h}{2} \\ t \geq 10 h\end{array}\right.
{
t
≤
12
−
2
h
t
≥
10
h
\newline
(c)
{
t
≥
12
−
h
2
10
t
≥
h
\left\{\begin{array}{l}t \geq 12-\frac{h}{2} \\ 10 t \geq h\end{array}\right.
{
t
≥
12
−
2
h
10
t
≥
h
\newline
(D)
{
t
≥
12
−
h
2
t
≥
10
h
\left\{\begin{array}{l}t \geq 12-\frac{h}{2} \\ t \geq 10 h\end{array}\right.
{
t
≥
12
−
2
h
t
≥
10
h
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