a hardware supplier manufactures three kinds of clamps, types A,B, and C. Production restrictions force it to make 10 more type C than the total of the the other types and three times as many type B clamps as type A clamps. The shop must produce 490 clamps per day. How many of each type are made per day?

A clamps produced?
B clamps produced?
C clamps produced?

Question

a hardware supplier manufactures three kinds of clamps, types A,B, and C. Production restrictions force it to make 10 more type C than the total of the the other types and three times as many type B clamps as type A clamps. The shop must  produce 490 clamps per day. How many of each type are made per day?

A clamps produced?
B clamps produced?
C clamps produced?

anonymous · Answer

Set up your equations like this:

C = A + B + 10
(C is 10 more than the total of the other two types)

B = 3A
(B is three times as many A)

A + B + C = 490
(The shop produces 490 clamps total)

Substitute the 2nd equation into the 1st.  Then put this simplified equation into the last.

That will allow you to solve for A, which then gets you B (using the 2nd equation), which then gets you C (using either the first of the last equations).