SOLUTION: There are 126 tourists staying at the hotel. The ratio of Germans to French is 3 : 1. The ratio of all other nationalities to French is 2 : 1. What is the total number of Germans

Question 1095102:
There are 126 tourists staying at the hotel. The ratio of Germans to French is 3 : 1. The ratio of all other nationalities to French is 2 : 1. What is the total number of Germans staying at the hotel?
Found 2 solutions by greenestamps, josmiceli:
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Let...
x = number of French tourists;
then...
2x = number of tourists of nationalities other than French or German; and
3x = number of German tourists

You could continue with formal algebra from here to solve the problem. However, with the expressions x, 2x, and 3x for the numbers of tourists in the three groups, it is clear that exactly half the tourists in the hotel are German.

So the number of Germans in the hotel is half the total of 126, or 63.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The 126 tourists are 3 types:
Let = the number of germans
Let = the number of French
Let = the number of all others
--------------------------------------

(1)
---------------------------

(2)
---------------------------
(3)
---------------------------
Plug (1) and (2) into (3)
(3)
(3)
(3)
and
(1)
(1)
and
(2)
(2)
-------------------
There are 63 Germans
------------------------
check:
(3)
(3)
(3)
OK

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