# Word Problem — System of Equations

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

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The second equation must be c = 10+a+b and not c=10+a+b+c –  satish ramanathan Mar 25 '14 at 0:39
Thanks so much! Pesky thing, that was. –  Learner Mar 25 '14 at 0:48

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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