Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

There are twice as many girls as boys at a school. If $30\%$ 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?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

For convenience assume there are $300$ learners, i.e. $200$ girls and $100$ boys.

$30\%$ of $200$ is $60$ and $45\%$ of $100$ is $45$ .

Thus, $60 + 45 = 105$ learners have completed their project.

The percentage of learners who still need to complete their project is thus
$\frac{300 - 105}{300} \times 100 = \frac{195}{3} = 65.$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.