Question: solving system of inequalities on integers


This question comes from a math forum, somebody wanted to solve the following system with maple, but he didn't find a way for it:

eqs:={20<=a,a<=60, 20<=b,b<=60, 20<=c,c<=60, 20<=d,d<=60, a+b+c+d=160, 4*a+6*b+8*c+12*d=1200};

where a,b,c,d are integers.

A possible workaround to try each a,b,c,d, numbers in the given ranges to find the solutions, but it would be good from maple to solve it directly.

Can Maple solve these kinds of problems directly?

Another remark: it would be also nice if maple could accept the 20<=a<=60 style input.

Thank you for your comments in advance.

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