Problem 5. At the city market, $3 \mathrm{~kg}$ of apples cost the same as $2 \mathrm{~kg}$ of pears, and $2 \mathrm{~kg}$ of pears cost the same as $1 \mathrm{~kg}$ of cherries. Georgi bought $5 \mathrm{~kg}$ of apples, Ivan bought $3 \mathrm{~kg}$ of cherries, and Filip bought $3 \mathrm{~kg}$ of pears. Who spent the most money? Explain your answer.
Solution. Since $3 \mathrm{~kg}$ of apples cost the same as $2 \mathrm{~kg}$ of pears, it follows that $15 \mathrm{~kg}$ of apples cost the same as $10 \mathrm{~kg}$ of pears. According to this, $5 \mathrm{~kg}$ of apples (one third of 15) cost more than $3 \mathrm{~kg}$ of pears (less than one third of 10). This means that George spent more money than Philip.

Furthermore, since $3 \mathrm{~kg}$ of apples cost the same as $1 \mathrm{~kg}$ of cherries, it follows that $6 \mathrm{~kg}$ of apples would cost the same as $2 \mathrm{~kg}$ of cherries, so we have that $5 \mathrm{~kg}$ of apples cost less than $2 \mathrm{~kg}$ of cherries, which in turn cost less than $3 \mathrm{~kg}$. This means that Ivan spent more money than George. According to this, Ivan spent the most money.

## V section