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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 11 chicken nugget kid meal, for a total of $5\$5. On Thursday, she spent $29\$29 on 33 hamburger kid meals and 44 chicken nugget kid meals. How much does each type of meal cost?\newlineEach hamburger meal costs $\$_____, and each chicken nugget meal costs $\$_____.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 11 chicken nugget kid meal, for a total of $5\$5. On Thursday, she spent $29\$29 on 33 hamburger kid meals and 44 chicken nugget kid meals. How much does each type of meal cost?\newlineEach hamburger meal costs $\$_____, and each chicken nugget meal costs $\$_____.
  1. Define Variables: Let xx be the cost of a hamburger meal and yy be the cost of a chicken nugget meal. From Monday's purchase, we have the equation y=5y = 5. From Thursday's purchase, we have the equation 3x+4y=293x + 4y = 29.
  2. Write Equations: Now we write the system of equations:\newline11. y=5y = 5\newline22. 3x+4y=293x + 4y = 29
  3. Substitute and Solve: We can use the first equation directly in the second equation since it's already solved for yy. So we substitute y=5y = 5 into the second equation to find xx.
  4. Simplify Equation: Substituting yy into the second equation gives us 3x+4(5)=293x + 4(5) = 29.
  5. Subtract and Solve: Simplify the equation: 3x+20=293x + 20 = 29.
  6. Find Value of x: Subtract 2020 from both sides to solve for xx: 3x=93x = 9.
  7. Find Value of x: Subtract 2020 from both sides to solve for xx: 3x=93x = 9.Divide both sides by 33 to find the value of xx: x=3x = 3.

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