there are 600 children on a field. 30% of them were boys. after 5 teams of boys join the children on the field, the percentage of children who were boys increaseto 40%. how many boys were there in the 5 teams altogether?
so we had .3(600) boys or 180 boys
let the number of boys that joined be x
so .4(600+x) = 180+x
solve for x
30% of 600 = 180
180+5n = .40(600+5n)
Now just find n and thus 5n.
To solve this problem, we need to break it down into steps:
Step 1: Find the total number of children on the field before the boys from the five teams join.
Given that 30% of the children were boys and there are 600 children on the field, we can find the total number of boys using the following equation:
Number of boys = 30% * Total number of children
Number of boys = 0.30 * 600
Number of boys = 180
So, there were 180 boys on the field before the boys from the five teams joined.
Step 2: Calculate the total number of children on the field after the boys from the five teams join.
Let's assume the total number of boys in the five teams is 'x'. Since there are 600 children on the field, the total number of children after the boys join will be:
Total number of children = 600 + x
Step 3: Calculate the percentage of boys after the boys join the field.
We are given that the percentage of boys after the five teams join is 40%. We can set up the following equation:
(180 + x) / (600 + x) = 40%
To solve this equation, we can convert the percentage into a decimal and then solve for 'x':
(180 + x) / (600 + x) = 0.40
Now we can solve for 'x' by cross-multiplying:
0.40(600 + x) = 180 + x
240 + 0.40x = 180 + x
0.40x - x = 180 - 240
-0.60x = -60
x = -60 / -0.60
x = 100
Step 4: Calculate the total number of boys in the five teams altogether.
Since each team consists of the same number of boys, we divide the total number of boys by the number of teams to get the number of boys in each team:
Number of boys in each team = 100 / 5
Number of boys in each team = 20
Therefore, there were 20 boys in each of the five teams, for a total of 20 * 5 = 100 boys altogether in the five teams.