TITLE: Word Problem -- System of Equations
QUESTION [0 upvotes]: 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

REPLY [0 votes]: 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, $\boxed{a = 40, \ b =80, \ c = 130}$.
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