SOLUTION: A hardware manufacturer makes 3 kinds of clamps, A, B, C. The production line makes 20 more C clamps than the total of the other types, and 3 times as many B clamps than type A. T

Question 452923: A hardware manufacturer makes 3 kinds of clamps, A, B, C. The production line makes 20 more C clamps than the total of the other types, and 3 times as many B clamps than type A. The shop must produce 420 clamps per day. How many of each clamp does the factory make daily?
I'd appreciate it if someone could help me. I can't even to begin to decipher this one. Thanks
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A hardware manufacturer makes 3 kinds of clamps, A, B, C.
The production line makes 20 more C clamps than the total of the other types,
and 3 times as many B clamps than type A.
The shop must produce 420 clamps per day. How many of each clamp does the factory make daily?
:
Here's how to decipher this one, write an equation for each statement
:
"The production line makes 20 more C clamps than the total of the other types,"
C + 20 = A + B
:
"and 3 times as many B clamps than type A."
B = 3A
:
"The shop must produce 420 clamps per day."
A + B + C = 420
:
We can replace A+B with C+20 (from the 1st statement)
C + 20 + C = 420
2C = 420 - 20
2C = 400
C = 200
:
Then we have
A + B = 420 - 200
A + B = 220
We know that B = 3A, therefore
A + 3A = 220
4A = 220
A =
A = 55
:
I'll let you find B, check that the solutions add up to 420

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