Ratios, rates and proportional reasoning

Packets of tea in a shop in Kampala: a $250$ g packet costs $5000$ shillings and a $400$ g packet costs $7600$ shillings. Which is the better buy?

A recipe for $6$ people uses $4$ cups of millet flour. How many cups are needed for $15$ people?

Mr Short is $4$ buttons tall and $6$ paper clips tall. Mr Tall is $10$ buttons tall. How many paper clips tall is Mr Tall?

Which of these relationships are proportional? (Choose all that apply.)

In a proportional relationship, $y = 7$ when $x = 2$, and $y = 17.5$ when $x = 5$. What is $y$ when $x = 12$?

A bicycle costs $200$ dollars. The price rises by $10\%$, and the next month the new price falls by $10\%$. What is the final price, in dollars?

In a sale everything is $20\%$ off. A jacket now costs $240$ reais. What was its price before the sale?

The population of a town rises by $25\%$. By what percentage must it then fall to return to its original size?

Which Lean definition says correctly that $f$ is proportional (there is one constant $k$ with $f(x) = kx$ for every $x$)?

Write constant_of_proportionality(table). The table is a list of pairs (x, y). Return the constant $k$ (as a Fraction) if $y = kx$ for every row, and None otherwise. Rows with x == 0 must have y == 0, and there must be at least one row with x != 0. Use Fraction so that decimals such as \"0.5\" are exact.