Chapter 1.2, Problem 66PPSE

Solution

To state: The two ways to compute the bill if there are five friends and each ordered a sandwich and a drink. The amount of each sandwich is same, similarly each drink cost the same.

The property illustrated by both the methods is Distributive property of real numbers.

Given information:

The given statement says that there are five friends and each ordered a sandwich and a drink. The amount of each sandwich is same, similarly each drink cost the same.

Explanation:

Consider the given situation:

Assume the cost of a sandwich is x and the cost of a drink is y .

Therefore, the two ways of calculating the bill are shown below:

First way:

Calculate the bill of each person: $\left(x+y\right)$

Now multiply it with number 5 to get the total bill: $5\left(x+y\right)$

Second way:

Find the cost of 5 sandwiches and 5 drinks and then add them.

Calculate the bill of 5 sandwiches: $5x$

Calculate the bill of 5 drinks: $5y$

Now add both to get the total bill: $5x+5y$

Both methods will get the same result because both methods are equivalent.

Therefore, $5\left(x+y\right)=5x+5y$ .

This relation is shown by the Distributive property $a\left(b+c\right)=ab+ac$ .