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, 2020

Algebra Difficulty 2.5 Junior Find the answer Canada

In Rad’s garden there are exactly 30 red roses, exactly 19 yellow roses, and no other roses. How many of the yellow roses does Rad need to remove so that $\frac{2}{7}$ of the roses in the garden are yellow?

$5$
$6$
$4$
$8$
$7$

Your answer

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

Solution

If $\frac{2}{7}$ of the roses are to be yellow, then the remaining $\frac{5}{7}$ of the roses are to be red.
Since there are 30 red roses and these are to be $\frac{5}{7}$ of the roses, then $\frac{1}{7}$ of the total number of roses would be $30 \div 5 = 6$ , which means that there would be $6 \times 7 = 42$ roses in total.
If there are 42 roses of which 30 are red and the rest are yellow, then there are $42 - 30 = 12$ yellow roses.
Since there are 19 yellow roses to begin, then $19 - 12 = 7$ yellow roses are removed.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.