+0  
 
0
63
1
avatar+420 

Larry has 4-cent stamps and 9-cent stamps, which he can combine to produce various amounts of postage. For example, he can make 40 cents by using four 9-cent stamps and a 4-cent stamp, or by using ten 4-cent stamps. However, there are some amounts of postage he can't make exactly, such as 10 cents.

What is the largest number of cents that Larry CANNOT make exactly from a combination of 4- and/or 9-cent stamps?

Explain how you know your answer is correct. (You should explain two things: why Larry can't make the amount of your answer, and why he CAN make any bigger amount.)

SmartMathMan  Jan 26, 2018
Sort: 

1+0 Answers

 #1
avatar+18927 
+1

Larry has 4-cent stamps and 9-cent stamps, which he can combine to produce various amounts of postage.
For example, he can make 40 cents by using four 9-cent stamps and a 4-cent stamp, or by using ten 4-cent stamps.
However, there are some amounts of postage he can't make exactly, such as 10 cents.

 

What is the largest number of cents that Larry CANNOT make exactly from a combination of 4- and/or 9-cent stamps?

 

Explain how you know your answer is correct. (You should explain two things:
why Larry can't make the amount of your answer, and
why he CAN make any bigger amount.)

 

\(\begin{array}{l} \cdots\{4\} \cdots \{8,9\}\cdots \{12,13\}\cdots \{16,17,18\} \cdots \{20,21,22\} \cdots {\color{red}23} \{\underbrace{24,25,26,27}_{\underset{27+4=31}{\underset{26+4=30,}{\underset{25+4=29,}{\underset{24+4=28,}{}}}} }\} \{\underbrace{28,29,30,31}_{\underset{31+4=35}{\underset{30+4=34,}{\underset{29+4=23,}{\underset{28+4=32,}{}}}} }\} \{\underbrace{32,33,34,35}_{\underset{35+4=39}{\underset{34+4=38,}{\underset{33+4=37,}{\underset{32+4=36,}{}}}} }\} \text{ and so on} \\\\ \{\text{reachable}\} \\ \cdots \text{not reachable}\\ \end{array} \)

 

23 is the largest number of cents that Larry CANNOT make exactly from a combination of 4- and/or 9-cent stamps.

After four consecutive reachable numbers, 24, 25, 26, 27, he CAN make any bigger amount.

 

laugh

heureka  Jan 26, 2018

14 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details