Question 1170240
<br>
You can of course practice using formal algebra to solve problems to get the answer to the problem.  And since this problem is presumably from a course in basic algebra, you should understand how to set up and solve the problem that way.<br>
But part of the purpose of studying mathematics is to develop problem solving skills in general.<br>
You can get some good practice at that by solving this problem with logical reasoning and a bit of mental arithmetic.<br>
Here is a quick solution without formal algebra.<br>
(1) The average cost is about $50/15 = $10/3, or about $3.33; that is closer to $3.63 than it is to $2.75.  So more chicken sandwich meals than hamburger meals were ordered.<br>
(2) The total cost was $50.05, which is a multiple of 5 cents.  The cost of each hamburger meal, $2.75, was also a multiple of 5 cents; so the total cost of the hamburger meals was a multiple of 5.<br>
That means the total cost of the chicken sandwich meals must be a multiple of 5; and since the cost of each one is $3.63, the number of chicken sandwich meals must be a multiple of 5.<br>
Putting (1) and (2) together, with a total of 15 meals being ordered, the answer has to be 10 chicken sandwich meals and 5 hamburger meals.<br>
ANSWER: 10 chicken sandwich meals (and 5 hamburger meals)<br>
CHECK: 10(3.63)+5(2.75) = 36.30+13.75 = 50.05<br>
For a typical setup using formal algebra....<br>
x = # of chicken sandwich meals
15-x = # of hamburger meals<br>
{{{(3.63)(x)+(2.75)(15-x) = 50.05}}}<br>
Solve using basic algebra....<br>
(But you can see the solution is going to take much more work than the one above using logical reasoning....)<br>