# ALGEBRA

A hardware supplier manufactures three kinds of clamps, type A, B, and C. Production restrictions force it to make 20 more type C clamps than the total of the other types and twice as many as B clamps as type A clamps. The shop must produce 380 clamps per day. How many of each type are made per day? How many type A clamps are produced?

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1. "three kinds of clamps, type A, B, and C"
Let A,B,C represent the number of each.

"20 more type C clamps than the total of the other types"
C=A+B+20

"twice as many as B clamps as type A clamps."
A=2B

"produce 380 clamps per day"
A+B+C=380

So in summary, the equations are:
A+B+C=380 ...(1)
C=A+B+20 ...(2)
A=2B ...(3)

This can be solved by successive substitution as follows:

A=2B => C=(2B)+B+20=3B+20
Substitute A and C in the first equation
(2B) + B + (3B+20) = 380
Solve for B:
6B=360
B=60
therefore
A=2B = 120
C=3B+20=200
Check: A+B+C=120+60+200=380 OK.

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