Kapalci

2022-06-20

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.

a. Write a system of inequalities to model this situation.

b. Graph the system.

c. Could he eat 3 hamburgers and 1 cookie?

d. Could he eat 2 hamburgers and 4 cookies?

I think the answer for question a is:

$\{\begin{array}{l}1.4h+0.5c\le 5\\ 240h+160c\ge 800\end{array}$

If I was to solve this by graphing, how will I know which would be the x and y variable?

a. Write a system of inequalities to model this situation.

b. Graph the system.

c. Could he eat 3 hamburgers and 1 cookie?

d. Could he eat 2 hamburgers and 4 cookies?

I think the answer for question a is:

$\{\begin{array}{l}1.4h+0.5c\le 5\\ 240h+160c\ge 800\end{array}$

If I was to solve this by graphing, how will I know which would be the x and y variable?

hofyonlines5

Beginner2022-06-21Added 12 answers

The second equation should be

$240h+160c\ge 800$

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

$100$

which is mathematically the same inequality and can be graphed in the same " order scale" as your first.

$240h+160c\ge 800$

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

$100$

which is mathematically the same inequality and can be graphed in the same " order scale" as your first.