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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineSamantha and her friend Mabel are each baking apple pies and tarts for a bake sale, using the same recipes. Samantha baked 77 apple pies and 88 apple tarts, using a total of 8888 apples. Mabel made 11 apple pie and 88 apple tarts, which used 4040 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.\newlineSamantha and her friend Mabel are each baking apple pies and tarts for a bake sale, using the same recipes. Samantha baked 77 apple pies and 88 apple tarts, using a total of 8888 apples. Mabel made 11 apple pie and 88 apple tarts, which used 4040 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 system of equations based on the given information.\newlineSamantha's baking: 77 pies and 88 tarts used 8888 apples.\newlineMabel's baking: 11 pie and 88 tarts used 4040 apples.\newlineThis gives us the two equations:\newline7x+8y=887x + 8y = 88 (Equation 11)\newline1x+8y=401x + 8y = 40 (Equation 22)
  3. Use Elimination: Use elimination to solve the system of equations.\newlineWe will eliminate xx by subtracting Equation 22 from Equation 11.\newline(7x+8y)−(1x+8y)=88−40(7x + 8y) - (1x + 8y) = 88 - 40\newline7x−1x+8y−8y=88−407x - 1x + 8y - 8y = 88 - 40\newline6x=486x = 48
  4. Solve for x: Solve for x.\newlineDivide both sides of the equation by 66 to find the value of xx.\newline6x6=486\frac{6x}{6} = \frac{48}{6}\newlinex=8x = 8
  5. Substitute and Solve: Substitute the value of xx into one of the original equations to solve for yy. Using Equation 22: 1x+8y=401x + 8y = 40 1(8)+8y=401(8) + 8y = 40 8+8y=408 + 8y = 40 8y=40−88y = 40 - 8 8y=328y = 32
  6. Solve for y: Solve for y.\newlineDivide both sides of the equation by 88 to find the value of yy.\newline8y8=328\frac{8y}{8} = \frac{32}{8}\newliney=4y = 4
  7. Final Answer: State the final answer.\newlineAn apple pie uses 88 apples and an apple tart requires 44 apples.

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