Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 1 hamburger kid meal and 3 chicken nugget kid meals, for a total of $14. On Thursday, she spent $36 on 4 hamburger kid meals and 7 chicken nugget kid meals. How much does each type of meal cost? Each hamburger meal costs $_____, and each chicken nugget meal costs $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 1 hamburger kid meal and  3 chicken nugget kid meals, for a total of $14. On Thursday, she spent $36 on 4 hamburger kid meals and  7 chicken nugget kid meals. How much does each type of meal cost?  Each hamburger meal costs $_____, and each chicken nugget meal costs $_____.

Bytelearn · Accepted Answer

Set up equations: Set up the system of equations based on the given information. On Monday, 1 hamburger meal (h) and 3 chicken nugget meals (c) cost $14. On Thursday, 4 hamburger meals (h) and 7 chicken nugget meals (c) cost $36. The system of equations is: 1h + 3c = 14 4h + 7c = 36Multiply first equation: Multiply the first equation by 4 to align the coefficient of h with the second equation. (1h + 3c) * 4 = 14 * 4 4h + 12c = 56Subtract equations: Subtract the second equation from the modified first equation to eliminate h and solve for c. (4h + 12c) - (4h + 7c) = 56 - 36 4h + 12c - 4h - 7c = 56 - 36 5c = 20Solve for c: Solve for c. 5c = 20 c = 20 / 5 c = 4Solve for h: Substitute the value of c back into the original first equation to solve for h. 1h + 3(4) = 14 1h + 12 = 14 1h = 14 - 12 h = 2Verify solution: Verify the solution by substituting both h and c into the second original equation. 4(2) + 7(4) = 36 8 + 28 = 36 36 = 36

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