SOLUTION: I don't understand this; x + 2y - z = 1 y = -x z= x + 1 ___________ ___________ ___________ ___________ ___________ ______ hotel oakwood charges $40 a night for two people

SOLUTION: I don't understand this; x + 2y - z = 1 y = -x z= x + 1 _____ _ _ _ _ hotel oakwood charges $40 a night for two people

Question 117572: I don't understand this;
x + 2y - z = 1
y = -x
z= x + 1
__________________________________________________________________
hotel oakwood charges $40 a night for two people plus $5 for each additional person. pine valley lodge charges $38 a night for two people plus $6 for each additional person.
a. write an equation for the cost y with x additional people in a room for one night at each place.
H.O. _______________________ P.V.L. ________________________
b. for how many people will the rate for the two rooms be the same?
_______________________________________________________________________________
three-bean salad can be made by mixing green, kidney, and wax beans. the recipe calls for the same amount of kidney beans and wax beans. and twice as much green beans as kidney beans. Let g be the number of cups of green beans, k the number of cups of kidney beans, and w the number of cups of wax beans, determine how much of each kind of bean should be used for nine cups of salad.
green_______________ kidney___________________ wax__________________
______________________________________________________________________________

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The first thing you have is three linear equations in three unknowns.

Since both of the 2nd and 3rd equations are already solved in terms of one of the variables, it looks like the substitution method is the best for solution of this system.
Use the definitions of y and z from equations 2 and 3 to substitute into equation 1

Now that you have a value for x, y and z can be solved by substituting into equations 2 and 3.

Check: . Yep.

*****************************

Since we are looking for the value of x that makes the two costs be the same:

So the cost is the same when 4 people (2 plus 2 extras) stay.

**************************
The variables are g, k, and w.
We know that the total number of cups of salad (the sum of the ingredients) is 9, so:

We also know that and

Solve this just like we solved the first problem -- substitute so that you get an equation in one variable

and

and

Check:

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