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g100num [7]
3 years ago
12

How many solutions are there to the equation 10= a + b + c with each of a, b, and c a whole number greater than or equal to zero

?
Mathematics
1 answer:
djverab [1.8K]3 years ago
4 0
If <em>a</em> is fixed and <em>b</em>,<em>c</em> are unknowns then the equation <em>b</em>+<em>c</em>=10-<em>a</em> has 11-<em>a</em> solutions. They are pairs (b,c): (0,10-a), (1,9-a), (2,8-a), ... (10-a,0). As <em>a</em> runs from 0 to 10 we have total number of solutions (11-0)+(11-1)+...(11-1)=11+10+...+1=(1+11)*11/2=66.
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Shortcut Conversion:

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