Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and fiveteen copper coins, how many different sums from 1¢ to 160¢ can he make with a combination of his coins?	Pick one:
A) 80  B) 85  C) 81  D) 160  E) 157
The total sum is 5*2 + 15*5= 
<gadget id="calculator">5*2 + 15*5</gadget>
<output>85</output>
85¢. If you can make each sum from 1 to 85 (1¢, 2¢, 3¢, ..., 85¢), then the answer would be 85 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 84¢ and 82¢ (since total sum is 85¢ we cannot remove 1¢ or 3¢ to get 84¢ or 82¢).   So, out of 85 sums 4 are for sure not possible, so the answer must be   85 - 4= 
<gadget id="calculator">  85 - 4</gadget>
<output>81</output>
81 sums or less. Only A fits.   Answer: 81.
<result>C</result>
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and fiveteen copper coins, how many different sums from 1¢ to 160¢ can he make with a combination of his coins?