Question

For these two review questions, I want to make sure I'm understanding the concept behind these.

1) A dessert stand sells candy bars for $2.00 and ice cream sandwiches for $3.00. If 100 of these were sold for $250, how many candy bars and ice cream sandwiches are sold? Set up the equations and solve

I think I am setting up these two as systems of linear equations right?

2) I have five different hats and 10 different coats. I want to take 3 of the hats and 7 of the coats with me on a trip. How many ways can I choose these items? Set up only.
Is this a permutations/combinations problem or a multiplication principle problem?

Answer 1

1. Candy bars -- x
sandwiches -- y

x + y = 100
2x + 3y = 250

I don't know what method you have learned to solve these,

elimination: I would multiply the first equation by 2 and subtract them
or
substitution: from the first, y = 100-x, now sub that into the 2nd

Answer 2

2. I don't think the order in which you choose the hats and the coats matters, so this is a combination.
So for the hats ----> C(5,3)
for the coats -----> C(10,7)
multiply them