the ratio of the number of students in class A, B and C is 3:7:8. if 10 students leave c and join b , the ratio of the number of students in b and c would be reversed. find the total number of students in classes a,b and c
Can I from a equation and solve? Please explain
A:B:C = 3:7:8
A:B+10:C-10 = 3:8:7
That means that
b/c = 7/8
(b+10)/(c-10) = 8/7
Solving that, we have
b=70
c=80
Now, you can figure a.
180
Yes, you can form an equation and solve it to find the total number of students in classes A, B, and C.
Let's denote the number of students in class A, B, and C as A, B, and C respectively.
According to the given information, the ratio of the number of students in class A, B, and C is 3:7:8. This can be written as:
A/B = 3/7 (equation 1)
B/C = 7/8 (equation 2)
Now, it is given that if 10 students leave C and join B, the ratio of the number of students in B and C would be reversed. So, we can form another equation based on this information:
(B + 10)/(C - 10) = 8/7 (equation 3)
We now have three equations (equation 1, equation 2, and equation 3) with three unknowns (A, B, and C).
To solve these equations, we can use a method called substitution. Let's solve equation 1 and equation 2 to express one variable in terms of another:
From equation 1,
A = (3/7)B
From equation 2,
C = (8/7)B
Now, substitute the values of A and C in equation 3:
(B + 10)/((8/7)B - 10) = 8/7
Cross-multiply to simplify:
7(B + 10) = 8((8/7)B - 10)
Simplify further:
7B + 70 = (64/7)B - 80
Multiply both sides of the equation by 7 to get rid of the denominators and simplify:
49B + 490 = 64B - 560
Combine like terms:
15B = 1050
Divide both sides by 15:
B = 70
Using this value of B, we can now find the values of A and C:
From equation 1:
A = (3/7)B = (3/7) * 70 = 30
From equation 2:
C = (8/7)B = (8/7) * 70 = 80
So, the total number of students in classes A, B, and C is: A + B + C = 30 + 70 + 80 = 180.