Question 723929

there were {{{387}}} nonfatal occupational injuries

let the boat-building injuries be {{{B}}},amusement park/arcade injuries be {{{A}}}, and iron foundry injuries be {{{I}}}

given:

{{{B+A+I=387}}}

{{{A=B+12}}}

{{{I=A+30}}}...substitute {{{A}}} ...=> {{{I=B+12+30}}}...=> {{{I=B+42}}}

{{{B+A+I=387}}}...plug in all values

{{{B+(B+12)+(B+42)=387}}}...solve for {{{B}}}

{{{3B+12+42=387}}}

{{{3B+54=387}}}

{{{3B=387-54}}}

{{{3B=333}}}

{{{B=333/3}}}

{{{highlight(B=111)}}}

now find {{{A}}} and {{{I}}}

{{{A=B+12}}}

{{{A=111+12}}}

{{{highlight(A=123)}}}


{{{I=B+42}}}

{{{I=111+42}}}

{{{highlight(I=153)}}}

check their sum:

{{{B+A+I=387}}}

{{{111+123+153=387}}}

{{{387=387}}}

check your solution: A= 127, B= 115, and I= 145
Am I right?

your equation: {{{B+(B+12)+(B+30)=387}}} ...you put {{{I=(B+30)}}}, but it is given that {{{I}}} had {{{30}}} more than {{{A}}}, or {{{I=A+30}}}

so, you need to put 
 
{{{B+A+(A+30)=387}}}

since also given that {{{A}}} had {{{12}}} more than {{{B}}}, we know that {{{A=B+12}}} and we go back to {{{I}}} and substitute {{{A}}} 

{{{I=A+30}}}...=>...{{{I=B+12+30=B+42}}}

now, plug it in equation
{{{B+(B+12)+(B+42)=387}}}