Lee has two tests to study for: Chemistry and French. She plans to study for up to 13h in total. She will spend at least 4 hours studying Chemistry and up to 6 hours studying French. Let x represent the number of hours she will spend studying Chemistry, and y the number of hours studying French. Which system of inequalities best represents this situation?
a) x+y</13, x>/4, y</6
b) x+y>/13, x<6, y>/4
c) xy</13, x>4, y<6
d) x+y</6+4, xy</13
x+y <= 13, because she will spend up to 13 hours studying.
x >= 4, because she will spend at least 4 hours studying chemistry.
y <= 6, because she will spend up to 6 hours studying French.
You have to look at the keywords - "up to," "at least," to determine which inequality to use.
The system of inequalities that best represents this situation is:
a) x + y < 13, x > 4, y < 6.
Here's why:
- The inequality x + y < 13 represents the condition that Lee plans to study for a total of up to 13 hours.
- The inequality x > 4 represents the condition that Lee plans to study Chemistry for at least 4 hours.
- The inequality y < 6 represents the condition that Lee plans to study French for up to 6 hours.
Together, these three inequalities capture all the given conditions for Lee's study plan.