There are 340 children at a park. 2/5 of the boys is equal to 4/7 of the girls. how many girls and how many boys are there at the park?
Let's represent the number of boys as 'b' and the number of girls as 'g'.
According to the question, 2/5 of the boys is equal to 4/7 of the girls.
So we can write the equation as:
(2/5) * b = (4/7) * g
To simplify this equation, we can cross-multiply:
7 * (2/5) * b = 4 * g
Multiplying across:
(14/5) * b = 4 * g
Now, let's simplify further by multiplying both sides of the equation by 5:
14 * b = 20 * g
Dividing both sides of the equation by 2, we get:
7 * b = 10 * g
Since we know that the total number of children is 340, we can write another equation:
b + g = 340
Now, we have the two equations:
7 * b = 10 * g
b + g = 340
To solve these equations, we can use the substitution method.
From the second equation, we can rewrite it as:
b = 340 - g
Substituting this value of 'b' into the first equation, we get:
7 * (340 - g) = 10 * g
Expanding the equation:
2380 - 7g = 10g
Combining like terms:
2380 = 17g
Dividing both sides of the equation by 17, we get:
g = 2380 / 17
g ≈ 140
Substituting this value of 'g' into the equation b = 340 - g, we get:
b = 340 - 140
b ≈ 200
So, there are approximately 200 boys and 140 girls at the park.
To find out how many girls and how many boys there are at the park, we can set up an equation based on the given information.
Let's assume the number of boys at the park is 'b', and the number of girls is 'g'.
According to the problem, 2/5 of the boys is equal to 4/7 of the girls. Therefore, we can write the equation:
(2/5) * b = (4/7) * g
To solve this equation, we need to find a common denominator. The least common multiple of 5 and 7 is 35.
Multiplying both sides of the equation by 35, we get:
35 * (2/5) * b = 35 * (4/7) * g
14b = 20g
So, we have the equation 14b = 20g.
Now, we know that there are a total of 340 children at the park. Therefore, the sum of boys and girls is equal to 340:
b + g = 340
From the equation above, we can express g in terms of b:
g = 340 - b
Substituting this value of g in the equation 14b = 20g, we get:
14b = 20(340 - b)
Now we can solve this equation for 'b'.
14b = 6800 - 20b
14b + 20b = 6800
34b = 6800
Dividing both sides of the equation by 34, we get:
b = 6800 / 34
b = 200
Now, we can substitute the value of b back into the equation b + g = 340:
200 + g = 340
g = 340 - 200
g = 140
So, there are 200 boys and 140 girls at the park.
b+g = 340
2/5 b = 4/7 g
2/5 b = 4/7 (340-b)
b = 200