In a school gym, the ratio of the number of boys to the number of girls was 4:3. After a 160 boys left the gym, the ratio became 4:5. How many girls was in the gym?
b/g = 4/3
(b-160)/g = 4/5
g = 300
300
300
These other posts are confusing me. Can we stay on topic?
60 girls
Where do you get 300?!!?!?!!?
HOW DO YOU EVEN FIT 300 GIRLS IN A GYM?!?!?!!?!??!
To solve this problem, we'll set up a system of equations.
Let's say that initially, the number of boys in the gym is B, and the number of girls is G.
According to the given ratio, the number of boys to girls is 4:3, which can be expressed as:
B/G = 4/3
After 160 boys left the gym, the new number of boys is B - 160. The number of girls remains the same, G.
The new ratio of boys to girls is 4:5, which can be expressed as:
(B - 160)/G = 4/5
Now we have two equations:
1) B/G = 4/3
2) (B - 160)/G = 4/5
To solve this system of equations, we can use substitution.
From the first equation, we can express B in terms of G as:
B = (4/3)G
Substituting this into the second equation:
((4/3)G - 160)/G = 4/5
Now we can solve for G by cross-multiplication:
5((4/3)G - 160) = 4G
Simplifying the equation:
20G/3 - 800 = 4G
Multiply both sides by 3 to get rid of the fraction:
20G - 2400 = 12G
Subtract 12G from both sides:
8G = 2400
Divide both sides by 8:
G = 300
Therefore, there were 300 girls in the gym.