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A caterer is determining how many forks she will need to buy for her upcoming event. Each adult needs 5 forks, and each child needs 2 forks. If the event will host 764 adults and children in all, and the caterer ordered 2,992 forks, how many adults and how many children are expected to attend? Choose 1 answer: (A) 207 adults and 557 children (B) 276 adults and 488 children (C) 488 adults and 276 children (D) 557 adults and 207 children

A caterer is determining how many forks she will need to buy for her upcoming event. Each adult needs \(5\) forks, and each child needs \(2\) forks. If the event will host \(764\) adults and children in all, and the caterer ordered 2,9922,992 forks, how many adults and how many children are expected to attend?\newlineChoose 11 answer:\newline(A) \(207\) adults and \(557\) children\newline(B) \(276\) adults and \(488\) children\newline(C) \(488\) adults and \(276\) children\newline(D) \(557\) adults and \(207\) children

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Q. A caterer is determining how many forks she will need to buy for her upcoming event. Each adult needs \(5\) forks, and each child needs \(2\) forks. If the event will host \(764\) adults and children in all, and the caterer ordered 2,9922,992 forks, how many adults and how many children are expected to attend?\newlineChoose 11 answer:\newline(A) \(207\) adults and \(557\) children\newline(B) \(276\) adults and \(488\) children\newline(C) \(488\) adults and \(276\) children\newline(D) \(557\) adults and \(207\) children
  1. Identify Variables: Let's denote the number of adults as AA and the number of children as CC. We are given two equations based on the problem statement:\newline11. Each adult needs 55 forks, and each child needs 22 forks.\newline22. The total number of adults and children is 764764.\newline33. The caterer ordered 2,9922,992 forks.\newlineWe can represent these as two equations:\newline5A+2C=2,9925A + 2C = 2,992 (Equation 11: Forks needed)\newlineA+C=764A + C = 764 (Equation 22: Total number of attendees)
  2. Solve Equation 22: We can solve these equations using the method of substitution or elimination. Let's use the elimination method. First, we'll solve Equation 22 for one of the variables. Let's solve for CC:C=764−AC = 764 - A
  3. Substitute CC into Equation 11: Now we substitute C=764−AC = 764 - A into Equation 11: 5A+2(764−A)=2,9925A + 2(764 - A) = 2,992
  4. Distribute and Simplify: We distribute the 22 in the second term and simplify the equation: 5A+1,528−2A=2,9925A + 1,528 - 2A = 2,992
  5. Combine Like Terms: Combine like terms: 3A+1,528=2,9923A + 1,528 = 2,992
  6. Isolate A Term: Subtract 1,5281,528 from both sides to isolate the term with AA: 3A=2,992−1,5283A = 2,992 - 1,528
  7. Calculate Right Side: Calculate the right side of the equation: 3A=1,4643A = 1,464
  8. Solve for A: Divide both sides by 33 to solve for A:\newlineA=1,4643A = \frac{1,464}{3}
  9. Calculate Value of A: Calculate the value of A:\newlineA=488A = 488
  10. Substitute AA into Equation 22: Now that we have the number of adults, we can find the number of children by substituting AA back into Equation 22:\newlineC=764−AC = 764 - A\newlineC=764−488C = 764 - 488
  11. Calculate Value of C: Calculate the value of C:\newlineC=276C = 276
  12. Final Solution: We have found the number of adults and children:\newlineA=488A = 488 adults\newlineC=276C = 276 children

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