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Algebra Difficulty 2.1 Junior Prove it Canada

Each day, Ella loaded her truck with red shirts and blue shirts
for delivery to two stores. At Store 1, she dropped off some shirts, and
at Store 2 she dropped off all remaining shirts.

On Monday, she loaded $800$ red shirts and $200$ blue shirts. At Store 1, she dropped
off only red shirts. At Store 2, $50\%$ of the shirts dropped off were red.
How many red shirts were dropped off at Store 1?
On Tuesday, she loaded $5x$ red shirts and $5x$ blue shirts. At Store 1, she dropped
off $40\%$ of the red shirts, and no
blue shirts. What percentage of the shirts dropped off at Store 2 were
blue?
On Wednesday, she loaded $3y$ red shirts and $y$ blue shirts. At Store 1, she dropped
off some red shirts and no blue shirts. Additionally, she picked up some
green shirts. At Store 2, she dropped off all remaining shirts and the
numbers of red, green, and blue shirts dropped off were equal. Of all
the shirts that she dropped off on Wednesday, determine the percentage
that were green.

Solution

At Store 2, $50\%$ of the
shirts dropped off were red, and so the other $50\%$ were blue.

That is, Ella dropped off an equal number of red and blue shirts at
Store 2.

All 200 blue shirts were dropped off at Store 2, and thus $200$ red shirts were also dropped off at
Store 2. Ella began the day with $800$ red shirts, dropped off $200$ at Store 2, and so she dropped off
$800-200=600$ red shirts at Store
1.
At Store 1, Ella dropped off $40\%$ of $5x$ red shirts or $0.40\times5x=2x$ red shirts.

Ella dropped off the remaining $5x-2x=3x$ red shirts at Store 2, in
addition to the $5x$ blue shirts. At
Store 2, $\dfrac{5x}{3x+5x}=\dfrac{5}{8}$ of the
shirts dropped off were blue, which is $\frac58\times100\%=62.5\%$ of the
shirts.
Ella dropped off no blue shirts at Store 1, and so she dropped
off all $y$ blue shirts at Store 2.
Since there were equal numbers of red, blue and green shirts dropped off
at Store 2, then $y$ green shirts
(and $y$ red shirts) were dropped off
at Store 2.

On Wednesday, Ella dropped off $3y$
red shirts, $y$ blue shirts, and
$y$ green shirts, for a total of
$5y$ shirts.

Of all the shirts dropped off on Wednesday, $\dfrac{y}{5y}=\dfrac{1}{5}$ were green,
which is $\frac15\times100\%=20\%$ of
the shirts.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

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