SOLUTION: Hello. I am stumped as to even beginning this question! All I am very sure of is that my answer cannot be any greater than 64. "Eight girls get off a school bus that has a seati

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Hello. I am stumped as to even beginning this question! All I am very sure of is that my answer cannot be any greater than 64. "Eight girls get off a school bus that has a seati      Log On


   

Question 827989: Hello. I am stumped as to even beginning this question! All I am very sure of is that my answer cannot be any greater than 64.
"Eight girls get off a school bus that has a seating capacity of 64 children. When they leave, the ratio of girls to boys becomes 3:4. When 5 boys get on the bus, the ratio of girls to boys becomes 7:11. How many students were initially on the bus?"
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"Eight girls get off a school bus that has a seating capacity of 64 children.
When they leave, the ratio of girls to boys becomes 3:4.
When 5 boys get on the bus, the ratio of girls to boys becomes 7:11.
How many students were initially on the bus?"
:
A lot of steps here, but each one is not too hard to understand, if you take some time to follow them.
:
Let g = number of girls initially\
let b = number of boys initially
:
""Eight girls get off a school bus that has a seating capacity of 64 children.
When they leave, the ratio of girls to boys becomes 3:4.
%28g-8%29%2Fb = 3%2F4
Cross multiply
3b = 4(g-8)
3b = 4g - 32
3b - 4g = -32, use this form to use elimination
" When 5 boys get on the bus, the ratio of girls to boys becomes 7:11."
%28g-8%29%2F%28b%2B5%29 = 7%2F11
Cross multiply
7(b+5) = 11(g-8)
7b + 35 = 11g - 88
7b = 11g - 88 - 35
7b = 11g - 123
7b - 11g = -123
:
Elimination with these two equations
3b - 4g = -32
7b - 11g = -123
Multiply the 1st equation by 7, multiply the 2nd equation by 3
21b - 28g = -224
21b - 33g = -369
---------------------subtraction eliminates b, find g
5g = +145
g = 145/5
g = 29 girls initially
find the boys using 3b = 4g - 32
3b = 4(29) - 32
3b = 84
b = 84/3
b = 28 boys
How many students were initially on the bus?"
29 + 28 = 57 students
:
You can confirm this by using these values to find the ratio's given