I'm studying high school algebra and the textbook had this question:
Omar needs to eat at least 800 calories before going to his team practice. All he wants is hamburgers and cookies, and he doesn’t want to spend more than \$5. At the hamburger restaurant near his college, each hamburger has 240 calories and costs \$1.40. Each cookie has 160 calories and costs \$0.50.
ⓐ Write a system of inequalities to model this situation.
ⓑ Graph the system.
ⓒ Could he eat 3 hamburgers and 1 cookie?
ⓓ Could he eat 2 hamburgers and 4 cookies?
I think the answer for question ⓐ is: \begin{equation} \left\{ \begin{array}{@{}ll@{}} 1.4h + 0.5c \le 5 \\ 240h + 160 c \ge 800 \end{array}\right. \end{equation}
If I was to solve this by graphing, how will I know which would be the x and y variable? Can someone please explain to me?
The second equation should be
$$240h + 160 c \ge 800$$ because he wants at least 800 calories, not at most.
You can use $h$ as the $x$-variable, and $c$ as the $y$ or the other way round. Your choice. It's just a name, just like you chose to name $h$ as the number of hamburgers (why not $x$?) etc.
Of course the graph is weird unit-wise: the first equation is about prices and the second about calories. Just ignore it, see them as numbers only, and scale the equations, e.g. dividing the above by $100$ already simplifies it to
$$2.4h + 1.6 c \ge 8$$ which is mathematically the same inequality and can be graphed in the same " order scale" as your first.