Question

A party organizer is determining how many plates she will need to buy for her upcoming event. Each adult needs 4 plates and each child needs 2 plates. If the event will host 750 adults and children in all, and the party organizer ordered 2582 plates, how many adults and how many children are expected to attend ?

• A. 193 adults & 557 children
• B. 241 adults & 509 children
• C. 541 adults & 209 children
• D. 555 adults & 195 children

Answer 1

The correct option is C 541 adults & 209 children

Let's say there are A adults and C children, then there are 4A plates for adults and 2C plates for children.

Lets form equations now

A + C = 750 .........(i)
4A + 2C = 2582 ........(ii)

Let's solve the above system of equations by elimination.
We can begin by multiplying equation (i) by 2.



Subtract that new equation from (ii)
4A + 2C = 2582
2A + 2C = 1500
______________
$2A=\frac{1082}{2}$

A = 541

Lets solve for C

Put A = 541 in first equation (i), we get

541 + C = 750

C = 750 - 541 = 209

Hence, option C is correct.