SOLUTION: A restaurant charges $3.50 for its “all you can eat” breakfast buffet, and $5.00 for its lunch buffet. At 2 PM the manager found that 100 people had eaten in the restaurant that d

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Question 908: A restaurant charges $3.50 for its “all you can eat” breakfast buffet, and $5.00 for its lunch buffet. At 2 PM
the manager found that 100 people had eaten in the restaurant that day, and the total receipts were $428.How many people had eaten breakfast and how many had eaten lunch? Solve this problem using any method, however to receive full credit, you must specify which method you are using and show supporting
work.
Answer by matwiz(2) (Show Source):
You can put this solution on YOUR website!
Let X be the people who ate breakfast, Y be the people who ate lunch
We know that
(a) x + y = 100
and that
(b) 3.50x + 5.00y = 428
for (a), I choose to rewrite it as y = 100-x
Thence we have for (b):
3.50x + 5.00(100 - x) = 428
3.5x + 500 - 5x = 428
-1.5x = - 72
x = 48 ate breakfast
y = 100 - 48 = 52 ate lunch
Check:
$3.50 x 48 + $5.00 x 52 = $168 + $260 = $428
The solution checks