Question

Nathan has two types of stamps:
4¢ stamps
8¢ stamps

Nathan has sheets and sheets of these stamps and that he won’t run out of them. Answer the following questions to consider how different combinations of stamps can be used.

A. Nathan plans to mail a postcard that requires 40¢ in postage. List all of the different ways that he could use the two types of stamps to total 40¢ in postage.

B. How can you be sure that you found all of the possible combinations?

C. If Nathan used a total of 8 stamps for the 40¢ in postage, how many of each type of stamp did he use? Show your work and explain how you arrived at your answer.

Answer 1

A. He could use 5 of the 8¢ Stamps 
    He could use 10 of the 4¢  Stamps 

B. You can be sure that you have found all of the possible combinations because those are the only sets of those specific numbers that equals 40¢ 

C. If Nathan used 40¢ worth of stamps in postage, given that 40¢ is all that Nathan is willing to spend, he would have only used the 8¢ variety of the stamps he owns. You can explain this reasoning in the fact that 8 x 5 = 40 and he spends 40¢.