Question

Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 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+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?

Answer 1

Answer:

$t \ge h$ and $t + 0.5h \le 12.0$

Step-by-step explanation:

Given

$t= thickness$

$h =height$

From the first statement, we have that:

$t\ mm \ge 0.1 * h\ cm$

Convert mm to cm

$t\ * 0.1*cm \ge 0.1 * h\ cm$

$t\ *0.1 \ge 0.1 * h$

Divide both sides by 0.1

$t \ge h$

From the second statement, we have that:

$Cost \le 12.2$

Substitute 0.2 + t + 0.5h for Cost

$0.2 + t + 0.5h \le 12.2$

Collect Like Terms:

$t + 0.5h \le 12.2-0.2$

$t + 0.5h \le 12.0$

So, the inequalities are:

$t \ge h$ and $t + 0.5h \le 12.0$