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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo 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 $131\$131 on 99 new shirts and 44 pairs of shorts. The older brother purchased 99 new shirts and 55 pairs of shorts and paid a total of $148\$148. How much did each item cost?\newlineEach shirt cost $____\$\_\_\_\_, and each pair of shorts cost $____\$\_\_\_\_.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo 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 $131\$131 on 99 new shirts and 44 pairs of shorts. The older brother purchased 99 new shirts and 55 pairs of shorts and paid a total of $148\$148. How much did each item cost?\newlineEach shirt cost $____\$\_\_\_\_, and each pair of shorts cost $____\$\_\_\_\_.
  1. Define Prices: Let's denote the price of each shirt as ss and the price of each pair of shorts as pp. The younger brother spent $131\$131 on 99 shirts and 44 pairs of shorts, which gives us the equation 9s+4p=1319s + 4p = 131.
  2. Younger Brother's Purchase: The older brother purchased 99 shirts and 55 pairs of shorts for a total of $148\$148, which gives us the equation 9s+5p=1489s + 5p = 148.
  3. Elimination Method: We now have a system of two equations. To use elimination, we need to eliminate one of the variables, ss or pp. Since the coefficients of ss are the same in both equations, we can eliminate ss by subtracting the first equation from the second.
  4. Calculate Shorts Price: Subtracting the first equation from the second, we get 9s+5p−(9s+4p)=148−1319s + 5p - (9s + 4p) = 148 - 131, which simplifies to p=17p = 17.
  5. Substitute and Solve: Now that we have the value of pp, we can substitute it back into the first equation to find the value of ss. Substituting p=17p = 17 into the first equation, we get 9s+4(17)=1319s + 4(17) = 131.
  6. Calculate Shirt Price: Solving for ss, we have 9s+68=1319s + 68 = 131. Subtracting 6868 from both sides, we get 9s=639s = 63.
  7. Final Prices: Dividing both sides by 99, we find that s=7s = 7. So, each shirt costs $7\$7.
  8. Final Prices: Dividing both sides by 99, we find that s=7s = 7. So, each shirt costs $7\$7.We have found that each shirt costs $7\$7 and each pair of shorts costs $17\$17.

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