Collin and Elizabeth are buying apparel at a store where all shirts are the same cost and all hats are the same cost. Collin buys 4 shirts and 3 hats and pays $\$ 118$. Elizabeth buys 4 shirts and 1 hat and pays $\$ 74$. [These prices do not include taxes.]
How much does each shirt and each hat cost?
- Each shirt: \$
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- Each hat: \$
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Answer
Final Answer: Each shirt costs \(\boxed{13}\) dollars and each hat costs \(\boxed{22}\) dollars.
Step 1 ：Let's denote the cost of a shirt as 's' and the cost of a hat as 'h'.
Step 2 ：From the problem, we can derive two equations: \(4s + 3h = 118\) (This is from Collin's purchase) and \(4s + h = 74\) (This is from Elizabeth's purchase).
Step 3 ：We can solve this system of equations to find the values of 's' and 'h'.
Step 4 ：The solution to the system of equations is {h: 22, s: 13}.
Step 5 ：Final Answer: Each shirt costs \(\boxed{13}\) dollars and each hat costs \(\boxed{22}\) dollars.
