Question 460027
A hardware supplier manufactures three kinds of clamps, types {{{A}}}, {{{B}}}, and{{{ C}}}. 

Production restrictions force it to make {{{20 }}}more tye {{{C}}} clamps than the total of the other types 

{{{ C=A+B+20}}}.

and twice as many type {{{B}}}clamps as type A clamps. 

{{{B=2A}}}

The shop must produce {{{380 }}}clamps per day. 

{{{ A+B+C=380}}}


How many of each type are made per day?

{{{ C=A+B+20}}}............1
{{{B=2A}}}.......................2....substitute in 1
{{{ A+B+C=380}}}...........3
---------------------------------------
{{{ C=A+2A+20}}}............1

{{{ C=3A+20}}}.............substitute in 3


{{{ A+2A+3A+20=380}}}...........3....solve for {{{A}}}

{{{ 6A=380-20}}}

{{{ 6A=360}}}

{{{ A=360/6}}}

{{{ highlight(A=60)}}}

{{{B=2A}}}.......................2

{{{B=2*60}}}

{{{highlight(B=120)}}}

{{{ C=3A+20}}}.

{{{ C=3*60+20}}}
{{{ C=180+20}}}.

{{{ highlight(C=200)}}}.


check:

{{{ A+B+C=380}}}

{{{ 60+120+200=380}}}

{{{ 380=380}}}