SOLUTION: The total number of​ restaurant-purchased meals that the average person will eat in a​ restaurant, in a​ car, or at home in a year is 141. The total number of the

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Question 1100280: The total number of​ restaurant-purchased meals that the average person will eat in a​ restaurant, in a​ car, or at home in a year is 141. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Ten more​ restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.
This one's a big one and it is pretty hard.
Found 3 solutions by josmiceli, ikleyn, richwmiller:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of meals eaten in a restaurant
Let = number of meals eaten in a car
Let = number of meals eaten at home
-------------------------------------------------
(1)
(2)
(3)
----------------------------
Substitute (3) into (1)
(1)
and
(2)
Substitute this into (1)
(1)
and
(3)
Substitute this into (1)
(1)
(1)
(1)
(1)
and
(3)
(3)
(3)
and
(2)
(2)
(2)
--------------------------
65 meals are eaten in a restaurant
21 meals are eaten in a car
55 meals are eaten at home
--------------------------------
check:
(1)
(1)
(1)
OK
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
From the condition you have these two equations


Home  + Car  + Restaurant = 141   (1)

(Home + Car) - Restaurant =  11   (2)   ("The total number of meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. ")

---------------------------------------Subtract eq(2) from eq(1). You will get

2*Restaurant = 141 - 11 = 130  ==========>  Restaurant =  = 65.


Thus one unknown is just found.  It is Restaurant = 65.


Now account that "Ten more​ restaurant-purchased meals will be eaten in a restaurant than at home."


It will give you immediately  Home = Restaurant - 10 = 65 - 10 = 55.


Finally, from eq(1)  Car = 141 - (65+55) = 141 - 120 = 21.

Answer.   Home = 55,   Restaurant = 65,   Car = 21.


=============================
Dear turor @richwmiller,

In response to your question,

I am not obliged to report you



But if you wish, I can continue in more calm tone: 

    I did it because I feel that my addition and contribution will be useful.

Also, since 
    - I am quite old and experienced;

    - I have quite good (if not to say "perfect") mathematical education;

    - I learned from the best teachers, from the best textbooks, from the best books-collections of mathematical school problems, 
      advanced problems, Olympiad level problems;

    - I know the school math subjects along and accross;

with all of this and because of all of it, I am able to make my decisions on my own,
without asking your permission and even without asking your opinion, and even in opposite to your opinion.


Also, I am too good tutor (as you said) to tolerate yours invectives against me calling my posts and solutions "trivial".


Sincerely . . .



Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Ikleyn,
What non trivial info did you add to josmiceli's solution?
The webmaster and owner of this website tells us: "Add your answer only if you feel you have something non trivial to add. "
Rich
No, you are not obligated to answer to me. But you will most likely be hearing from Igor if you insist on adding your trivial responses. You are too good a tutor to troll about with duplicate answers. You are better than that.
Ikleyn,
I am referring to this problem of the total number of​ restaurant-purchased meals . Your solution added nothing to jocimeli's solution. You both had the same approach and the same answers.
I do not have an invective against you.
You are taking this much too personally.

Rich


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