An astronomer noted that a grouping of red giant stars had an average solar mass of 8 M each, and a grouping of white dwarf stars had an average solar mass of 1.5 M each. If the astronomer calculated the total solar mass of both groupings to be 49 M, what total number of red giant stars and white dwarf stars did the astronomer note? Select: A) 10 B) 11 C) 12 D) 13 E) 14
We can determine quickly that total number should range between 49/8 &lt;= N &lt;=49/1.5 , so ans should be between 6 and 33.   Now solving the expression 8A+1.5B =49   decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5. this way we get   2 red giants, 22 white dwarfs we get 49, but   2 + 22= 
<gadget id="calculator">  2 + 22</gadget>
<output>24</output>
24 and 24 is not an option.   Next we get 5 red giants and 6 white dwarfs to get 49, 5*8 + 6*1.5= 49   Hence total number is  5 + 6= 
<gadget id="calculator"> 5 + 6</gadget>
<output>11</output>
11   Ans 11
<result>B</result>
An astronomer noted that a grouping of red giant stars had an average solar mass of 8 M each, and a grouping of white dwarf stars had an average solar mass of 1.5 M each. If the astronomer calculated the total solar mass of both groupings to be 49 M, what total number of red giant stars and white dwarf stars did the astronomer note?