A customer wants to mail a package. The postal clerk

determines the cost of the package to be $18.95, but
only 6�‘ and 9�‘ stamps are available. Can the available
stamps be used for the exact amount of postage for the
package? Why or why not?

To determine if the available stamps can be used for the exact amount of postage for the package, we need to see if there is a combination of 6�‘ and 9�‘ stamps that adds up to $18.95.

Let's try to find a solution using a systematic approach:

1. Start by assuming the customer uses x number of 6�‘ stamps and y number of 9�‘ stamps.

2. The value of x 6�‘ stamps is 6x, and the value of y 9�‘ stamps is 9y.

3. We need the total value of stamps to equal $18.95. So, we can write the equation: 6x + 9y = 18.95.

4. One way to solve this equation is to try plugging in different values of x and y and see if we get a solution. In this case, let's start by checking x = 1 and y = 1:

6(1) + 9(1) = 6 + 9 = 15 (less than 18.95)

5. This combination didn't work, so let's try another one. Let's check x = 2 and y = 1:

6(2) + 9(1) = 12 + 9 = 21 (more than 18.95)

6. This combination didn't work either. Now, let's check x = 1 and y = 2:

6(1) + 9(2) = 6 + 18 = 24 (more than 18.95)

7. None of the combinations we've tried so far has given us the exact amount of $18.95. Now, we can conclude that the available 6�‘ and 9�‘ stamps cannot be used for the exact amount of postage for the package.

In summary, after systematically checking all possible combinations, we have determined that the available stamps cannot be used to achieve the exact amount of postage of $18.95.