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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent on new shirts and pairs of shorts. The older brother purchased new shirts and pairs of shorts and paid a total of . How much did each item cost?Each shirt cost _____, and each pair of shorts cost _____.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent on new shirts and pairs of shorts. The older brother purchased new shirts and pairs of shorts and paid a total of . How much did each item cost?Each shirt cost _____, and each pair of shorts cost _____.
- Define Prices: Let's denote the price of one shirt as and the price of one pair of shorts as . The younger brother's purchase can be represented by the equation:s + p =
- Younger Brother's Purchase: Similarly, the older brother's purchase can be represented by the equation:
- Older Brother's Purchase: We now have a system of equations:We can use either substitution or elimination to solve this system. Let's use elimination to solve for one of the variables.
- System of Equations: To eliminate , we can subtract the second equation from the first:(s + p) - (s + p) = - s - s + p - p = - s =
- Elimination Method: Now we can solve for :s = s = / s = So, each shirt costs \(9\).
- Solve for s: With the price of each shirt known, we can substitute \( s = 9 \) into one of the original equations to find \( p \). Let's use the second equation:\(\newline\)\(7\)s + \(7\)p = \(154\)\(\newline\)\(7\)(\(9\)) + \(7\)p = \(154\)\(\newline\)\(63\) + \(7\)p = \(154\)
- Substitute for p: Now we solve for \( p \):\(\newline\)\(7\)p = \(154\) - \(63\)\(\newline\)\(7\)p = \(91\)\(\newline\)p = \(91\) / \(7\)\(\newline\)p = \(13\)\(\newline\)So, each pair of shorts costs .
