Question

Hello there! Can I get some help please? Make sure you give enough explanation and show your work. I wanna know how to solve this kind of problems.

Five friends each ordered a sandwich and a drink at a restaurant. Each sandwich costs the same amount and each drink costs the same amount. What are two ways to compute the bill? What property of real numbers is illustrated by the two methods?

Answer 1

Hello,

We know that the cost of a sandwich is 1s (we call "s" the unknown variable of sandwich) and the cost of a drink is 1d (we call "d" the unknown variable of drinks). 5 friends order those sandwiches and drinks. For example, a sandwich may cost $1.00 and a drink $1.50. Now, the total of only one friend would be found by summing the price of a sandwich and the price of a drink. Then the total for one friend is given by 1s + 1d (or simply s + d).


Let's suppose they all buy the same sandwich and the same drink, they would all pay $1.00 and $1.50. We substitute the values s = $1.00 and d = $1.50

The total of all the sandwiches and drinks ordered by all the friends is given by 5 times the sandwiches (since they order five sandwiches) and 5 times the drinks (since they order five drinks).

So, one way to compute it is summing the sandwiches and drinks. 5s + 5d

Now, one friends pays a total of $1.00 + $1.50 = $2.50

Since they all pay $2.50, you multiply the total for 5.

This means the second way to compute this is 5(s + d)

This is called distributive property, where you group a common factor (in this case 5) and divide all terms by 5.

Then, once you have the factored result, just multiply 5 for each term in the parenthesis.

Hope this helped ^^

Answer 2

I think I can answer the first part, but jeez that second part is WAY too confusing for me to explain.

Two ways to compute the bill could be to take the bill for both the drink and sandwich that each of the five friends got and multiply it by five OR you could add all the bills for each person together and put it into one bill. A third way to compute the bill would be to take the cost of the sandwich that each person chose and multiply them by five, and take the cost of the drink and multiply them by five, and add both totals together.

Personally, I think the first option is the easiest. I don't know why anyone would purposely chose the harder way, but y'know there's some pretty weird people on this planet.