Question

1. 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?

a. 207 adults and 557 children
b. 276 adults and 488 children
c. 488 adults and 276 children
d. 557 adults and 207 children

Explanation:

Step1: Define variables

Let $a$ = number of adults, $c$ = number of children.

Step2: Set up total people equation

$a + c = 764$ → $c = 764 - a$

Step3: Set up total forks equation

$5a + 2c = 2992$

Step4: Substitute $c$ into fork equation

$5a + 2(764 - a) = 2992$

Step5: Simplify and solve for $a$

$5a + 1528 - 2a = 2992$
$3a = 2992 - 1528 = 1464$
$a = \frac{1464}{3} = 488$

Step6: Calculate number of children

$c = 764 - 488 = 276$

Answer:

C. 488 adults and 276 children