There are thrice as many girls as boys at a school. If 35% of the girls and 45% of the boys
have already completed their holiday project, what percentage of the learners still needs to
complete their project?
x(g+b) have not finished
.65 g have not finished
.55 b have not finished
.65 g + .55 b = x(g+b)
but
g = 3 b
so
.65(3 b)+.55 b = x ( 4 b )
(1.95+.55)b = 4 x b
x = 2.5/4 = .625
so
62.5 %
To find the percentage of learners who still need to complete their project, we first need to determine the ratio of girls to boys at the school.
Let's assume there are 'x' boys at the school. Since there are thrice as many girls as boys, the number of girls would be 3x.
Now, let's calculate the number of girls who have completed their holiday project. The percentage of girls who have completed their project is 35%, so the number of girls who have completed their project is 0.35 * (3x) = 1.05x.
Similarly, let's calculate the number of boys who have completed their holiday project. The percentage of boys who have completed their project is 45%, so the number of boys who have completed their project is 0.45 * x = 0.45x.
To find the total number of learners who have completed their project, we add the number of girls and boys who have completed their project: 1.05x + 0.45x = 1.5x.
The total number of learners at the school is the sum of the number of girls and boys: 3x + x = 4x.
Therefore, the percentage of learners who have completed their project is (1.5x / 4x) * 100% = 37.5%.
To find the percentage of learners who still need to complete their project, subtract this percentage from 100%: 100% - 37.5% = 62.5%.
Therefore, 62.5% of the learners still need to complete their holiday project.