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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineThe drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 99 regular gift baskets and 33 deluxe gift baskets, earning a total of $297\$297. During the spring musical, they sold 11 deluxe gift basket, earning a total of $45\$45. How much are they charging for the different sized gift baskets?\newlineThe drama club is charging $\$____\_\_\_\_ for a regular gift basket and $\$____\_\_\_\_ for a deluxe gift basket.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineThe drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 99 regular gift baskets and 33 deluxe gift baskets, earning a total of $297\$297. During the spring musical, they sold 11 deluxe gift basket, earning a total of $45\$45. How much are they charging for the different sized gift baskets?\newlineThe drama club is charging $\$____\_\_\_\_ for a regular gift basket and $\$____\_\_\_\_ for a deluxe gift basket.
  1. Write Equations: Let rr be the price of a regular gift basket and dd be the price of a deluxe gift basket. We can write two equations based on the information given: \newline11. For the fall play: 9r+3d=2979r + 3d = 297 \newline22. For the spring musical: d=45d = 45
  2. Create Augmented Matrix: To solve using an augmented matrix, we first write the coefficients of rr and dd in matrix form. The augmented matrix is:\newline \begin{array}{cc|c} 9 & 3 & 297 \ 0 & 1 & 45 \end{array}
  3. Substitute and Solve: Since the second row already shows that d=45d = 45, we can use this value to find rr. We substitute dd into the first equation: \newline9r+3(45)=2979r + 3(45) = 297
  4. Find rr: Now we solve for rr: \newline9r+135=2979r + 135 = 297\newline9r=297−1359r = 297 - 135\newline9r=1629r = 162
  5. Final Answer: Divide both sides by 99 to find rr:r=1629r = \frac{162}{9}r=18r = 18

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