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 ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?	Choose the correct choice.
A) 66  B) 67  C) 68  D) 69  E) 70
The total sum is 10*2 + 10*5= 
<gadget id="calculator">10*2 + 10*5</gadget>
<output>70</output>
70¢. If you can make each sum from 1 to 70 (1¢, 2¢, 3¢, ..., 70¢), then the answer would be 70 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 69¢ and 67¢ (since total sum is 70¢ we cannot remove 1¢ or 3¢ to get 69¢ or 67¢).   So, out of 70 sums 4 are for sure not possible, so the answer must be   70 - 4= 
<gadget id="calculator">  70 - 4</gadget>
<output>66</output>
66 sums or less. Only A fits.   66nswer: 66.
<result>A</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 ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?