在一间商店里，5 顶相同的帽子和 14 条相同的腰带的价格与 1 顶帽子和 26 条腰带的价格相同。每顶帽子比每条腰带贵 $24。求一顶帽子的价格。 答: $ ___

1. Compare the two scenarios to find the relationship between the cost of hats and belts.

Since $5$ hats and $14$ belts cost the same as $1$ hat and $26$ belts, we can remove $1$ hat and $14$ belts from both sides of the balance.
$4$ hats cost the same as $12$ belts.
Therefore, $1$ hat costs the same as $3$ belts.

2. Use the price difference to find the cost of a belt.

We are given that $1$ hat costs $\char36{}24$ more than $1$ belt.
Since $1$ hat is equivalent to $3$ belts, the difference in cost between $3$ belts and $1$ belt is $\char36{}24$.
$2$ belts = $\char36{}24$
$1$ belt = $\char36{}24 \div 2 = \char36{}12$

3. Calculate the cost of a hat.

Cost of $1$ hat = $\char36{}12 + \char36{}24 = \char36{}36$
(Alternatively, $3 \times \char36{}12 = \char36{}36$)