I think I'm doing this wrong. Can anyone help me identify the problem? Thanks.
A hardware supplier manufactures three kinds of clamps, types A, B, and C. Production restrictions force it to make 10 more type C clamps than the total of the other types and twice as many type B clamps as type A clamps. The shop must produce 250 clamps per day. How many of each type are made per day?
My system of equations formed:
a+b+c=250 c=10+a+b+c b=2a
Well, first of all, your second equation should be $$ c = a + b + 10 $$ So essentially you get $$ 2a = b $$ $$ c = a+ b+ 10 $$ $$ a+b+c = 250 $$ Plugging the first into the second, we get: $$ c = 3a + 10 $$ Plugging this and the first into the third, we get: $$ a+ 2a + 3a + 10 = 250 \Rightarrow a = 40 $$
Therefore, $\boxed{a = 40, \ b =80, \ c = 130}$.