There were 352 children at a concert.
After 2/5 of the girls and 1/2 of the boys left, there remained equal amounts of boys and girls. How many girls remain
number of girls ---- x
number of boys ---- 352 - x
after the departures:
number of girls remaining = (3/5)x
number of boys remaining = (1/2)(352-x)
these are equal, so
(3/5)x = (1/2)(352-x)
times 10
6x = 5(352-x)
6x = 1760 - 5x
11x = 1760
x = 160
girls remaining = (3/5)x = ....
Let's break down the information provided step-by-step to find the number of girls that remain.
Step 1: Start with the total number of children at the concert, which is 352.
Step 2: Assuming the number of boys and girls are equal before any of them left, we can divide 352 by 2 to find the initial number of each gender.
352 / 2 = 176
So, initially, there were 176 boys and 176 girls at the concert.
Step 3: Calculate the number of girls who left. It is given that 2/5 of the girls left the concert.
(2/5) * 176 = 70.4
Since we cannot have a fractional number of children, we need to round up because even if a fraction of a child left, we would still consider it as one child.
Rounding up 70.4 gives us 71 girls who left the concert.
Step 4: Calculate the number of boys who left. It is given that 1/2 of the boys left the concert.
(1/2) * 176 = 88
So, 88 boys left the concert.
Step 5: Subtract the number of girls who left (71) and the number of boys who left (88) from the initial number of girls (176) to find the remaining number of girls.
176 - 71 = 105
Therefore, 105 girls remain at the concert.
To find the number of girls remaining, let's break down the problem step by step:
1. Start with the total number of children at the concert, which is 352.
2. We know that there were boys and girls at the concert, but we don't know the specific number for each group. So, let's use variables to represent them: let's say there were 'g' girls and 'b' boys.
3. After 2/5 of the girls left, the number of remaining girls can be calculated as (3/5)g.
4. Similarly, after 1/2 of the boys left, the number of remaining boys can be calculated as (1/2)b.
5. The problem states that after these departures, there remained equal amounts of boys and girls. So, (3/5)g = (1/2)b.
Now let's solve this equation to find the value of 'g' (the number of girls remaining).
(3/5)g = (1/2)b
To simplify the equation, we can multiply both sides by 10 to get rid of the fractions:
10 * (3/5)g = 10 * (1/2)b
Simplifying further, we have:
6g = 5b
Now, we need to find values for 'g' and 'b' that satisfy this equation and consider the total number of children, which is 352.
We can find the values that satisfy this equation by trying different values for 'b' and calculating the corresponding 'g' values. We need to find values that are both integers and make the equation true while also ensuring that the sum of 'g' and 'b' equals 352.
One possible solution is:
Let's say there were 160 boys (b = 160). Substituting this value for 'b' in the equation:
6g = 5(160)
6g = 800
g = 800 / 6
g ≈ 133.33
However, since we need an integer value for 'g', this solution is not possible.
Let's try another solution:
Let's say there were 200 boys (b = 200). Substituting this value for 'b' in the equation:
6g = 5(200)
6g = 1000
g = 1000 / 6
g ≈ 166.67
Since we need an integer value for 'g', this solution is also not possible.
Continuing to try different values for 'b', we find that when there are 240 boys (b = 240), we get:
6g = 5(240)
6g = 1200
g = 1200 / 6
g = 200
Since this solution satisfies the equation, we have found that there were 200 girls remaining after 2/5 of the girls and 1/2 of the boys left.