SOLUTION: 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and Engli
Algebra.Com
Question 174573: 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and English, and 300 are enrolled in Math and History. How many of the 500 students are enrolled in all three?
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x="students enrolled in all three"
"170 are enrolled in both Math and English" __ so 170-x are enrolled in ONLY Math and English
"150 are enrolled in both History and English" __ so 150-x are enrolled in ONLY History and English
"300 are enrolled in Math and History" __ so 300-x are enrolled in ONLY Math and History
"500 students are enrolled in at least two of these three classes"
so (170-x)+(150-x)+(300-x)+x = 500
620-2x=500
120=2x
60=x
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
500 students are enrolled in at least two of these three classes: Math,
English, and History. 170 are enrolled in both Math and English,
150 are enrolled in both History and English, and 300 are enrolled in
Math and History.
How many of the 500 students are enrolled in all three?
:
Let x = no. students enrolled in all three
:
These students are represented in an equal amt in all three groups:
:
The equation for students taking only two subjects
(170-x) + (150-x) + (300-x) = 500 - x
620 - 3x + x = 500
-2x = 500 - 620
-2x = -120
x = +60 students take all three subjects
:
Check solution
170 - 60 = 110 students taking Math & Eng only
150 - 60 = 90 students taking Hist & Eng only
300 - 60 = 240 students taking Math & Hist only
All 3 sub = 60 students
----------------
Tot stud =500
;
:
RELATED QUESTIONS
500 students are enrolled in at least two of these three classes: Math, English, and... (answered by rapaljer)
16. 30 people are having lunch at my house. 16 of them want salads, 16 of them prefer... (answered by 303795)
Please help me solve this word problem about Compound Events:(union, intersection and... (answered by math_tutor2020,ikleyn)
A survey at a certain school shows that 20% of the students are enrolled in Math, 23% are (answered by richwmiller)
At a liberal arts college in the Midwest, 39% of freshman are enrolled in both a math... (answered by math_tutor2020)
How would I solve this problem: at a highschool, 85 students are enrolled in fine arts.... (answered by fractalier,Boreal,ikleyn)
An elementary school is offering two optional language classes, one in French and the... (answered by ikleyn)
In a group of 28 students, 11 are taking math, 19 are taking English, 12 are taking... (answered by Greenfinch)
There are 100 students enrolled in various AP courses at American High School. There are... (answered by ikleyn)