Question 299379
a) 


Let s = price per shirt, p = price per pair of pants



Since they "purchased 15 work shirts and 10 pairs of work pants for its production line workers at a cost of $300", we know that {{{15s+10p=300}}}. Note: 15s is the total cost of 15 shirts and 10p is the total cost of 10 pants. Simply add these together to get 300.



Similarly, we're given that "they purchased an additional 12 work shirts and 17 pairs of work pants for $402" which means that {{{12s+17p=402}}}



So we now have the system


{{{system(15s+10p=300,12s+17p=402)}}}



{{{17(15s+10p)=17(300)}}} Multiply the both sides of the first equation by 17.



{{{255s+170p=5100}}} Distribute and multiply.



{{{-10(12s+17p)=-10(402)}}} Multiply the both sides of the second equation by -10.



{{{-120s-170p=-4020}}} Distribute and multiply.



So we have the new system of equations:

{{{system(255s+170p=5100,-120s-170p=-4020)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(255s+170p)+(-120s-170p)=(5100)+(-4020)}}}



{{{(255s+-120s)+(170p+-170p)=5100+-4020}}} Group like terms.



{{{135s+0p=1080}}} Combine like terms.



{{{135s=1080}}} Simplify.



{{{s=(1080)/(135)}}} Divide both sides by {{{135}}} to isolate {{{s}}}.



{{{s=8}}} Reduce.



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{{{255s+170p=5100}}} Now go back to the first equation.



{{{255(8)+170p=5100}}} Plug in {{{s=8}}}.



{{{2040+170p=5100}}} Multiply.



{{{170p=5100-2040}}} Subtract {{{2040}}} from both sides.



{{{170p=3060}}} Combine like terms on the right side.



{{{p=(3060)/(170)}}} Divide both sides by {{{170}}} to isolate {{{p}}}.



{{{p=18}}} Reduce.



So the solutions are {{{s=8}}} and {{{p=18}}}.



This means that an individual shirt costs $8 and a single pair of pants costs $18


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b) 



Now because they want "to buy 25 work shirts and 40 pairs of work pants", this means that the total cost of 25 shirts is {{{25*8=200}}} dollars and the total cost of 40 pants is {{{40*18=720}}} dollars. Add this up to get {{{200+720=920}}} dollars.



So the total cost of 25 work shirts and 40 pairs of pants is $920. Since {{{920<950}}}, this means that they will have enough money.