SOLUTION: Hi There were 2 classes A and B. 3/4 of the students in A and 5/8 in B passed a test. An equal number of students in both classes failed the test. If there was a total of 84 passe

Question 1204798: Hi
There were 2 classes A and B. 3/4 of the students in A and 5/8 in B passed a test. An equal number of students in both classes failed the test. If there was a total of 84 passes,what was the total number of students in both classes.
Thanks

Found 4 solutions by math_tutor2020, mananth, josgarithmetic, greenestamps:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Class A: 3/4 passed, 1/4 failed
Class B: 5/8 passed, 3/8 failed

x = number of students in class A
y = number of students in class B

(1/4)x = number in class A that failed
(3/8)y = number in class B that failed
(1/4)x = (3/8)y
4*(1/4)x = 4*(3/8)y
x = 1.5y
We'll use this in a substitution step later.

(3/4)x = number in class A who passed
(5/8)y = number in class B who passed
(3/4)x+(5/8)y = total number of passing grades
(3/4)x+(5/8)y = 84
8*((3/4)x+(5/8)y) = 8*84
6x+5y = 672

Plug in the previous equation we found earlier.
6x+5y = 672
6*1.5y+5y = 672
9y+5y = 672
14y = 672
y = 672/14
y = 48 people in class B
(3/8)y = (3/8)*48 = 18 people in class B failed the test, and it's also the number of people who failed in class A.

There are 48-18 = 30 people who passed in class B.

(1/4)x = number who failed class A's test
(1/4)x = 18
x = 4*18
x = 72 people in class A
72 - 18 = 54 people passed in class A
Or we could write it as:
(3/4)x = (3/4)*72 = 54 people passed in class A

Ultimately there are x+y = 72+48 = 120 students total

Summary Table

Class A Class B Total
Passed 54 30 84
Failed 18 18 36
Total 72 48 120

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

There were 2 classes A and B. 3/4 of the students in A and 5/8 in B passed a test. An equal number of students in both classes failed the test. If there was a total of 84 passes,what was the total number of students in both classes.

There were 2 classes A and B
Let class A have A students
class B have B students

3/4 of the students in A and 5/8 in B passed a test.
1/4 A failed in class A and 3/8 B failed in class B
An equal number of students in both classes failed the test.
1/4 A = 3/8 B
8A=12B
divide by 4
2A=3B
2A-3B=0--------------------------------(1)
there was a total of 84 passes
3/4 A +5/8 B =84
multiply equation by 8
6A +5B =672------------------------------(2)
Multiply (1) by 3 and subtract from (2)
6A +5B =672
6A-9B=0
--------------
14 B = 672
B= 48
2 A = 3B
2A = 3*48
A = 3*48/2= 72
The total number of students in both classes is A+B=72+48=120

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
This helps make clear what is going on with the described information:

CLASS COUNT STUDENTS PASS FAIL A a (3/4)a (1/4)a B b (5/8)b (3/8)b TOTAL 84

The number of fails of each class was given as they were equal.

Solve this system in whatever way you want.

from that,
.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

In class A, 3/4 passed, so the ratio of pass to fail was 3:1.

In class B, 5/8 passed, so the ratio of pass to fail was 5:3, or 5/3:1.

Let x be the number in each class who failed.

Then the number who passed in class A was 3x, and the number who passed in class B was (5/3)x.

The total number of passes was 84:

The total number in class A was x+3x = 18+54 = 72.
The total number in class B was x+(5/3)x = 18+30 = 48.

ANSWER: The total number in the two classes was 72+48 = 120.

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