At a festival, 2/7 of the number of girls was equal to 3/5 of the number of the boys. There were 165 fewer boys than girls, how many children were at the festival in all?
b = g-165
2/7 g = 3/5 b
(b,g) = (150,315)
b = g - 165
2 g/7 = 3 b/5
2 g/7 = (3/5)(g-165)
solve for g
then for b
then add b+g
Um... I really didn't understand you very clearly. So can you like go through this so I can understand cause I'm not really fimillar with algerbra.
There are g girls and b boys.
2 g/7 = (3/5)(g-165)
(See Damon's derivation)
(10/21)g = g - 165
11/21 g = 165
g = 315
b = 315 -165 = 150
Total = b + g = 465
Um... How exactly did you find the number of girls? Sorry I don't understand algebra that much.
To solve this problem, we need to break it down into smaller steps.
Let's assume the total number of girls at the festival is represented by "G" and the total number of boys is represented by "B."
According to the first statement, "2/7 of the number of girls was equal to 3/5 of the number of boys." This can be written as:
(2/7) * G = (3/5) * B
Next, we are told that "there were 165 fewer boys than girls." We can express this as:
B = G - 165
Now we have a system of two equations:
(2/7) * G = (3/5) * B ---(Equation 1)
B = G - 165 ---(Equation 2)
To solve this system of equations, we can substitute Equation 2 into Equation 1:
(2/7) * G = (3/5) * (G - 165)
Now we can solve for G, the number of girls.
First, simplify the equation by multiplying both sides by the least common multiple (LCM) of 7 and 5, which is 35:
35 * (2/7) * G = 35 * (3/5) * (G - 165)
Simplifying further:
10 * G = 21 * (G - 165)
Distribute:
10 * G = 21 * G - 21 * 165
Combine like terms:
10 * G - 21 * G = - 21 * 165
Simplify:
- 11 * G = - 21 * 165
Divide both sides by -11 to isolate G:
G = (- 21 * 165) / (-11)
Now we can calculate the value of G:
G = 315
So, the total number of girls at the festival is 315.
To find the number of boys, we can substitute this value back into Equation 2:
B = 315 - 165
B = 150
Therefore, the total number of boys at the festival is 150.
To find the total number of children, we add the number of girls and boys together:
Total number of children = 315 (girls) + 150 (boys)
Total number of children = 465
Therefore, there were 465 children at the festival in total.