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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineJackie and her friend Isabelle are each baking apple pies and tarts for a bake sale, using the same recipes. Jackie baked 66 apple pies and 44 apple tarts, using a total of 7272 apples. Isabelle made 77 apple pies and 99 apple tarts, which used 110110 apples. How many apples does each dessert require?\newlineAn apple pie uses _\_ apples and an apple tart requires _\_ apples.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineJackie and her friend Isabelle are each baking apple pies and tarts for a bake sale, using the same recipes. Jackie baked 66 apple pies and 44 apple tarts, using a total of 7272 apples. Isabelle made 77 apple pies and 99 apple tarts, which used 110110 apples. How many apples does each dessert require?\newlineAn apple pie uses _\_ apples and an apple tart requires _\_ apples.
  1. Define Variables: Define the variables for the number of apples used in each dessert.\newlineLet xx be the number of apples used in one apple pie.\newlineLet yy be the number of apples used in one apple tart.
  2. Write Equations: Write the equations based on the given information.\newlineJackie baked 66 apple pies and 44 apple tarts using 7272 apples, which gives us the equation:\newline6x+4y=726x + 4y = 72\newlineIsabelle made 77 apple pies and 99 apple tarts using 110110 apples, which gives us the equation:\newline7x+9y=1107x + 9y = 110
  3. Set Up System: Set up the system of equations to solve using elimination.\newlineWe have the following system:\newline6x+4y=726x + 4y = 72\newline7x+9y=1107x + 9y = 110
  4. Multiply Equations: Multiply the first equation by 77 and the second equation by 66 to align the coefficients of xx for elimination.\newline(7)(6x+4y)=7(72)(7)(6x + 4y) = 7(72)\newline(6)(7x+9y)=6(110)(6)(7x + 9y) = 6(110)\newlineThis gives us:\newline42x+28y=50442x + 28y = 504\newline42x+54y=66042x + 54y = 660
  5. Eliminate x: Subtract the second equation from the first to eliminate x.\newline(42x+28y)−(42x+54y)=504−660(42x + 28y) - (42x + 54y) = 504 - 660\newline42x+28y−42x−54y=−15642x + 28y - 42x - 54y = -156\newline−26y=−156-26y = -156
  6. Solve for y: Solve for y.\newline−26y=−156-26y = -156\newliney=−156−26y = \frac{-156}{-26}\newliney=6y = 6
  7. Substitute for x: Substitute the value of yy into one of the original equations to solve for xx. Using the first equation: 6x+4(6)=726x + 4(6) = 72 6x+24=726x + 24 = 72 6x=72−246x = 72 - 24 6x=486x = 48 x=48/6x = 48 / 6 x=8x = 8
  8. Verify Solution: Verify the solution by substituting xx and yy into the second original equation.7(8)+9(6)=1107(8) + 9(6) = 11056+54=11056 + 54 = 110110=110110 = 110The solution is verified.

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