Question 908
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