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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe Sheppard family and the Malone family are seeing a movie together in the theater. At the concession stand, Mr. Sheppard paid $38\$38 for 33 large popcorns and 44 large drinks that his family will share. Mrs. Malone bought 33 large popcorns and 33 large drinks and paid $33\$33. How much does each item cost?\newlineA large popcorn costs $____\$\_\_\_\_ and a large drink costs $____\$\_\_\_\_.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe Sheppard family and the Malone family are seeing a movie together in the theater. At the concession stand, Mr. Sheppard paid $38\$38 for 33 large popcorns and 44 large drinks that his family will share. Mrs. Malone bought 33 large popcorns and 33 large drinks and paid $33\$33. How much does each item cost?\newlineA large popcorn costs $____\$\_\_\_\_ and a large drink costs $____\$\_\_\_\_.
  1. Set up equations: Step 11: Set up the equations based on the information given.\newlineMr. Sheppard's purchase: 3P+4D=383P + 4D = 38\newlineMrs. Malone's purchase: 3P+3D=333P + 3D = 33\newlineHere, PP represents the price of one large popcorn and DD represents the price of one large drink.
  2. Use elimination: Step 22: Use elimination to solve the system of equations.\newlineSubtract the second equation from the first to eliminate PP:\newline(3P+4D)(3P+3D)=3833(3P + 4D) - (3P + 3D) = 38 - 33\newlineThis simplifies to:\newlineD=5D = 5
  3. Substitute value: Step 33: Substitute the value of DD back into one of the original equations to find PP.\newlineUsing the second equation: 3P+3(5)=333P + 3(5) = 33\newline3P+15=333P + 15 = 33\newline3P=33153P = 33 - 15\newline3P=183P = 18\newlineP=183P = \frac{18}{3}\newlineP=6P = 6

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