Question 44687: There are 26 students in fifth grade class. All of the students speak either Spanish or Japanesee, and some speak both languages. If 18 of the students speak Spanish and 14 can speak Japanese, How many speak both Spanish and Japanese and how many speak Spanish, but not Japanese?
Found 3 solutions by stanbon, checkley71, josmiceli:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are 26 students in fifth grade class. All of the students speak either Spanish or Japanesee, and some speak both languages. If 18 of the students speak Spanish and 14 can speak Japanese, How many speak both Spanish and Japanese and how many speak Spanish, but not Japanese?
This is a Venn Diagram Problem.
Draw a rectangle and indicate there are 26 students in it.
Draw two intersecting circles in the rectangle.
14 speak Japanese and 18 speak Spanish. That adds up to 32 which
is 6 more that there are sudents. So put a 6 in the intersection
of the two circle. This represents the students who speak both
languages.
Label one of the circles Spanish and the other circle Japanese.
The Spanish circle needs to have 18 students in it so there must
be 18-6=12 who speak Spanish but do not speak Jananese.
The Jananese circle needs to have 14 students in it so there must
be 14-6=8 students who speak Japanese and do not speak Spanish.
See the picture?
Cheers,
Stan H.
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! 18+14=32 LANGUAGES SPOKEN BY 26 STUDENTS THUS THERE MUST BE 32-26=6 WHO SPEAK BOTH LANGUAGES. SPANISH BUT NOT JAPANESE IS 18-6=12 ONLY SPEAK SPANISH
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! Draw 2 circles that overlap. One circle contains the
18 students that speak Spanish. There are are no Spanish
speakers outside this circle. The other circle contains
the 14 Japanese speakers, with no Japanese speakers
outside the circle.
Ther are only 26 students, but 18 + 14 = 32 languages being
spoken among them.
s = Spanish spoken only
b = Spanish and Japanese spoken
j = Japanese only
s + b + b + j = 32
b + b languages are spoken by b students
s + b + j = 26
s + b = 18
j + b = 14
----------------------
18 + j = 26
j = 8
s + 14 = 26
s = 12
12 + 2b + 8 = 32
2b = 12
b = 6
----------------------
so, 6 students speak both languages
and 12 speak only Spanish
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