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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEvelyn likes to make desserts for bake sales. Last month, she made 22 batches of brownies and 11 batch of cookies, which called for 99 eggs total. The month before, she baked 22 batches of brownies and 22 batches of cookies, which required a total of 1212 eggs. How many eggs did Evelyn use for a batch of each dessert?\newlineEvelyn uses _\_ eggs to make a batch of brownies and _\_ eggs to make a batch of cookies.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEvelyn likes to make desserts for bake sales. Last month, she made 22 batches of brownies and 11 batch of cookies, which called for 99 eggs total. The month before, she baked 22 batches of brownies and 22 batches of cookies, which required a total of 1212 eggs. How many eggs did Evelyn use for a batch of each dessert?\newlineEvelyn uses _\_ eggs to make a batch of brownies and _\_ eggs to make a batch of cookies.
  1. Define variables: Let's define two variables: let bb be the number of eggs used for a batch of brownies, and let cc be the number of eggs used for a batch of cookies. We can write two equations based on the information given:\newline11. For the first month: 2b+1c=92b + 1c = 9 (two batches of brownies and one batch of cookies used 99 eggs)\newline22. For the month before: 2b+2c=122b + 2c = 12 (two batches of brownies and two batches of cookies used 1212 eggs)
  2. Write equations: Now, we will use the elimination method to solve the system of equations. We can do this by subtracting the first equation from the second equation to eliminate the variable bb.\newline(2b+2c)−(2b+1c)=12−9(2b + 2c) - (2b + 1c) = 12 - 9\newlineThis simplifies to:\newline2c−1c=32c - 1c = 3
  3. Use elimination method: Solving the simplified equation gives us the number of eggs used for a batch of cookies: c=3c = 3
  4. Solve for cookies: Now that we know the value of cc, we can substitute it back into one of the original equations to find the value of bb. Let's use the first equation:\newline2b+1c=92b + 1c = 9\newlineSubstituting c=3c = 3, we get:\newline2b+1(3)=92b + 1(3) = 9
  5. Substitute back: Solving for bb, we subtract 33 from both sides of the equation:\newline2b+3=92b + 3 = 9\newline2b=9−32b = 9 - 3\newline2b=62b = 6
  6. Solve for brownies: Dividing both sides by 22 gives us the number of eggs used for a batch of brownies: \newlineb=62b = \frac{6}{2}\newlineb=3b = 3

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