At a festival, 2/7 of the number of girls was equal to 3/5 of the number of boys. There were 165 fewer boys than girls. How many children were at the festival in all?
number of boys ---- b
number of girls ----- g
(2/7)g = (3/5)b
g = (3/5)(7/2)b = 21/10 b
g - b = 165
21b/10 - b = 165
21b - 10b = 1650
11b = 1650
b = 150
g = 21/10(150) = 315
150 boys, 315 girls, total of 465
check:
(2/7)(315 = 90
(3/5)(150) = 90
yeahhh
Can you simplify it to 6th grader terms
To solve this problem, let's break it down step by step:
Let's assume the number of girls at the festival is represented by the variable "g" and the number of boys is represented by the variable "b."
From the given information, we can deduce two equations:
1. The ratio of girls to boys: (2/7)g = (3/5)b
2. The difference in the number of boys and girls: b = g - 165
Now, let's solve these equations to find the value of "g."
First, let's simplify equation 1 by cross-multiplying:
5(2g) = 7(3b)
10g = 21b
Next, let's substitute equation 2 into the simplified equation 1 to eliminate "b":
10g = 21(g - 165)
Now, let's distribute and solve for "g":
10g = 21g - 3465
11g = 3465
g = 315
Now that we know the number of girls, we can substitute this value back into equation 2 to find the number of boys:
b = g - 165
b = 315 - 165
b = 150
To find the total number of children at the festival, we add the number of girls and boys together:
Total = g + b
Total = 315 + 150
Total = 465
Therefore, there were 465 children at the festival in total.