At a shop, the price of 5 identical hats and 14 identical belts is the same as the price of 1 hat and 26 belts. Each hat costs $24 more than each belt. Find the cost of a hat. Ans: $ ___

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, $3 \times \char36{}12 = \char36{}36$)