ah. sorry about that! i think i made a careless mistake :(( (even tho, of course i care! :))
g = number of girls;
b = number of boys.
Because the ratio of girls to boys is 3:1, therefore
g = 3b (1)
finally, we have
g-1 girls because one girl dropped the class;
b+3 boys because three more boys signed up.
Because the new ratio of girls to boys is 5:2, therefore
(g - 1)/(b + 3) = 5/2
2(g - 1) = 5(b + 3)
2g - 2 = 5b + 15
2g - 5b = 17 (2)
Substitute (1) into (2) to obtain
2(3b) - 5b = 17
b = 17
g = 3b = 3*17 = 51
Final number of students in the class = 17 + 51 = 68
Let A and B be the amount of money Alice and Bob have, respectively, at the beginning. We know that
A + n = 4(B - n)
A - n = 3(B + n)
Simplifying, we have
A + 5n = 4B
A = 3B + 4n
Subtracting the first equation from the second gives 5n = B - 4n, so B = 9n. Substituing this into the first equation gives A + n = 4(9n - n), from which we get A = 31n.
Therefore, the desired ratio is A/B = 31n/9n = 31/9.
hope this helped !
sorry! i just wrote out all my work but it randomly got deleted. the answer is 8. here's how i got it:
first, i formulated two equations using the world problem:
x + y = 30
2x = 3y = 5.
then, i isolated the variables and used subsitution, then algebra, to find the value of y (which was 11, but it doesn't matter which you find first). then i found out x (which is 19). then, i found the positive difference. so the equation would be 19 - 11 = 8.