Right answer- Let the total number of people in the group initially be x, and let the number of girls initially be g. We know two things: 1. Initially, 10% of the group are girls, so: g = 0.1x 2. After two girls leave and two boys arrive, 30% of the group are girls. The new total number of people in the group is x (the original group size), plus 2 boys, and the number of girls is g - 2. Thus: 0.3(x + 2) = g - 2 Now we substitute g = 0.1x into the second equation: 0.3(x + 2) = 0.1x - 2 Simplify and solve for x: 0.3x + 0.6 = 0.1x - 2 0.3x - 0.1x = -2 - 0.6 0.2x = -2.6 x = -2.6 / 0.2 = 13 So the total number of people in the group initially is 13. Now, using g = 0.1x, the number of girls initially is: g = 0.1 * 13 = 1.3 (girls=g) Since the number of girls must be a whole number, there seems to be an issue with how the percentages are interpreted in real-life context.
Right answer-
Let the total number of people in the group initially be x, and let the number of girls initially be g.
We know two things:
1. Initially, 10% of the group are girls, so:
g = 0.1x
2. After two girls leave and two boys arrive, 30% of the group are girls. The new total number of people in the group is x (the original group size), plus 2 boys, and the number of girls is g - 2. Thus:
0.3(x + 2) = g - 2
Now we substitute g = 0.1x into the second equation:
0.3(x + 2) = 0.1x - 2
Simplify and solve for x:
0.3x + 0.6 = 0.1x - 2
0.3x - 0.1x = -2 - 0.6
0.2x = -2.6
x = -2.6 / 0.2 = 13
So the total number of people in the group initially is 13. Now, using g = 0.1x, the number of girls initially is:
g = 0.1 * 13 = 1.3
(girls=g)
Since the number of girls must be a whole number, there seems to be an issue with how the percentages are interpreted in real-life context.
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