SOLUTION: Lauren is planning a catered dinner party for her parents with a budget of 396.00. She has selected two options: a chicken dinner that costs 9 dollars a plate and a steak dinner th

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Question 1204117: Lauren is planning a catered dinner party for her parents with a budget of 396.00. She has selected two options: a chicken dinner that costs 9 dollars a plate and a steak dinner that cost 12 dollars a plate. Lauren is working on the guests list and must also determine how many of each meal to order. Set up an equation and solve.
Found 4 solutions by mananth, MathTherapy, greenestamps, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
A chicken dinner that costs 9 dollars a plate
Let the number of plates she orders be x
A steak dinner that cost 12 dollars a plate
Let the number of plates she orders be y
She has a budget of 396.00

With more details we can go ahead with calculations.



Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Lauren is planning a catered dinner party for her parents with a budget of 396.00. She has selected two options:
a chicken dinner that costs 9 dollars a plate and a steak dinner that cost 12 dollars a plate. Lauren is working
on the guests list and must also determine how many of each meal to order. Set up an equation and solve. 

Using a DIOPHANTINE-EQUATION process, there are 12 possibilities, from 0 (zero) chicken and 33 steak dinners to 44
chicken and 0 (zero) steak dinners. There are 5 instances in which the number of steak dinners exceed the number of
chicken dinners, so obviously, the other 7 instances would be where the number of chicken dinners exceed the number
of steak dinners. As a result, some other clue/info. would need to be provided in order to have 1 (one) UNIQUE solution.

BTW: The equation you're looking for is 9C + 12S = 396, with the number of chicken and steak dinners being C, and S,
respectively. If additional info. is provided, it can be "tied" into the above equation, and one equation can be had,
in order to determine that one unique solution set.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The problem is poorly written. In real life, if the budget is $396, it would mean that the MAXIMUM you could spend is $396. In that case, solving the problem would involve an inequality rather than an equation. However, since the instructions say to write and solve an equation, it appears that we are supposed to spend the whole $396.

But then there are many combinations of chicken and steak dinners that will cost a total of $396, so we can't "solve" the problem in the sense of finding "the" answer.

So to work the problem we need to (1) assume that we are spending the whole $396 and (2) we are looking for the solution set and not "the" solution.

Let C be the number of chicken dinners and S be the number of steak dinners. Then the total cost of $396 is $9 for each chicken dinner plus $12 for each steak dinner:




This is a linear Diophantine equation -- there are two unknowns and only a single equation, with the number of solutions being limited by the fact that the unknowns have whole number values.

There are formal methods for finding the set of solutions; but in this case perhaps a more informal method using logical reasoning is appropriate.

The maximum number of chicken dinners is if there are no steak dinners:





The maximum number of steak dinners is if there are no chicken dinners:





So two solutions to the problem are 44 chicken dinners and 0 steak dinners, and 0 chicken dinners and 33 steak dinners.

We can find the other solutions by seeing that the cost of 4 chicken dinners is the same as the cost of 3 steak dinners. So, given any solution that spends the whole $396, we can find another solution by increasing the number of chicken dinners by 4 and decreasing the number of steak dinners, or the other way around.

Doing that, we get the following solution set of values (C,S):

(44,0)
(40,3)
(36,6)
(32,9)
(28,12)
(24,15)
(20,18)
(16,21)
(12,24)
(8,27)
(4,30)
(0,33)

That's 12 possible combinations of chicken and steak dinner that will spend the entire $396 budget.

To get "AN" answer to the problem, we would need to have another piece of information.
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.

How this  " problem "  is worded,  printed,  posted and presented,  it is not a  Math problem,  at all.

It is a typical soup of words of the type  " bring me that I don't know what ".


I really regret that such  " problems "  (such gibberish)  do appear on this forum.

Their right place is a garbage bin.



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