posted by ROSE .
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?
"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"
"twice as many as B clamps as type A clamps."
"produce 380 clamps per day"
So in summary, the equations are:
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:
A=2B = 120
Check: A+B+C=120+60+200=380 OK.