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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineMalone's Bakery sold one customer 11 dozen chocolate cookies and 1010 dozen oatmeal cookies for $76\$76. The bakery also sold another customer 1010 dozen chocolate cookies and 55 dozen oatmeal cookies for $95\$95. How much do the cookies cost?\newlineA dozen chocolate cookies cost $\$_____, and a dozen oatmeal cookies cost $\$_____.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineMalone's Bakery sold one customer 11 dozen chocolate cookies and 1010 dozen oatmeal cookies for $76\$76. The bakery also sold another customer 1010 dozen chocolate cookies and 55 dozen oatmeal cookies for $95\$95. How much do the cookies cost?\newlineA dozen chocolate cookies cost $\$_____, and a dozen oatmeal cookies cost $\$_____.
  1. Define variables: Define the variables for the cost of a dozen chocolate cookies and a dozen oatmeal cookies.\newlineLet xx be the cost of a dozen chocolate cookies and yy be the cost of a dozen oatmeal cookies.
  2. Write first equation: Write the equation for the first customer's purchase.\newline11 dozen chocolate cookies and 1010 dozen oatmeal cookies cost $76\$76.\newline1×x+10×y=761 \times x + 10 \times y = 76\newlinex+10y=76x + 10y = 76
  3. Write second equation: Write the equation for the second customer's purchase.\newline1010 dozen chocolate cookies and 55 dozen oatmeal cookies cost $95\$95.\newline10×x+5×y=9510 \times x + 5 \times y = 95\newline10x+5y=9510x + 5y = 95
  4. Eliminate variable xx: Choose which variable to eliminate.\newlineWe will eliminate xx by multiplying the first equation by −10-10 and the second equation by 11 to make the coefficients of xx opposite.\newline−10(x+10y)=−10(76)-10(x + 10y) = -10(76)\newline10x+5y=9510x + 5y = 95
  5. Multiply first equation: Multiply the first equation by -10＂).\(\newline\$-10x - 100y = -760\)
  6. Add equations: Add the modified first equation to the second equation to eliminate \(x\).\[(-10x - 100y) + (10x + 5y) = -760 + 95\]\[-10x + 10x - 100y + 5y = -760 + 95\]\[0x - 95y = -665\]\[-95y = -665\]
  7. Solve for y: Solve for y.\(\newline\)Divide both sides by \(-95\) to find the cost of a dozen oatmeal cookies.\(\newline\)\(y = -665 / -95\)\(\newline\)\(y = 7\)
  8. Substitute for \(x\): Substitute the value of \(y\) into the first equation to solve for \(x\).
    \(x + 10(7) = 76\)
    \(x + 70 = 76\)
    \(x = 76 - 70\)
    \(x = 6\)
  9. Verify solution: Verify the solution by substituting \(x\) and \(y\) into the second equation.\[10(6) + 5(7) = 95\]\[60 + 35 = 95\]\[95 = 95\]The solution is verified.

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