Solving Inequalities and Quadratic story problems

[Cup0fDOOM]

Question 1:

A hospital dietitian wishes to prepare a corn-bean vegetable dish which will provide at least 40 grams of carbs, and cost no more than \$0.36 per serving.

28 grams of corn provide 8 grams of carbs and cost \$.04.

30 grams of beans provide 5 grams of carbs and cost \$.03. For taste there must be at least 56 grams of beans. There must be at least as much corn as beans.

I need to find 5 inequalities and graph them, I know how to graph and solve the inequalities I'm just having a really hard time finding the inequalities.

What I have so far: corn > or equal to 56, amount of Corn > or equal to amount of Beans.

Question 2:

Montenia takes a commuter train to her restaurant every afternoon, traveling 25 miles. Later that evening she returns home on the same train, except it is able to average 5mph faster. Montenia spend a total of 1 hour and 50 minutes total on the trains commuting. what is the speed of the train on the return trip.

I know that the 25 is the constant term but I'm having issues with the other pieces of the problem.

What I would really like is for someone to walk be through it so I can understand it myself, so in the future I won't need someone to hold my hand.

 

[Jameson]

Hi Cup0fDOOM,

Welcome to MHB! :)

I'll help you out with #2.

We start with $d=rt$.

a) To model the trip there we can say that $d=r_1 \times t_1$ and on the way back we can say that $d=r_2 \times t_2$. Well now we have two equations but 5 variables, so we need to make some substitutions!

b) We know that \(\displaystyle t_1+t_2=\frac{11}{6}\), making note that 1 hour plus 5/6 of another hour is 11/6 hours.

c) We notice as well that $r_1+5=r_2$. With the previous two equations we can reduce the two times into one time and the two rates of travel into 1 rate. Lastly plug in 25 for $d$ and you should be able to solve.

Try that out and if you have any problems let me know :)

Jameson

 

[CaptainBlack]

Question 1:

A hospital dietitian wishes to prepare a corn-bean vegetable dish which will provide at least 40 grams of carbs, and cost no more than \$0.36 per serving.

28 grams of corn provide 8 grams of carbs and cost \$.04.

30 grams of beans provide 5 grams of carbs and cost \$.03. For taste there must be at least 56 grams of beans. There must be at least as much corn as beans.

I need to find 5 inequalities and graph them, I know how to graph and solve the inequalities I'm just having a really hard time finding the inequalities.

What I have so far: corn > or equal to 56, amount of Corn > or equal to amount of Beans.

Introduce two variables \(b\) and \(c\) for the number of grams per serving of beans and corn respectivly.

Then starting from the bottom:

There must be at least as much corn as beans: \(c \ge b \), or rearranging \( c-b\ge 0\)

There must be at least 56 grams of beans: \( b\ge 56 \)

Now you need inequalities for cost and carbs, try to do these yourself and if you have trouble post again in this thread for more help.

Also there must be a non-negative quantity of corns, so \(c \ge 0\)

CB