SOLUTION: I know the basic idea of solving this, but cannot for the life of me set up the original equation to get me started. THANKS! in April Ricky's rockers purchased 15 work shirts an

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Question 299379: I know the basic idea of solving this, but cannot for the life of me set up the original equation to get me started. THANKS!
in April Ricky's rockers purchased 15 work shirts and 10 pairs of work pants for its production line workers at a cost of $300. then again in august they purchased an additional 12 work shirts and 17 pairs of work pants for $402.
a) how much was each work shirt and each pair of work pants
b) next year rickys rockers plans to buy 25 work shirts and 40 pairs of work pants. if they budgeted $950 next year will they have enough funds to purchase the shirst and pants?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B10p=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%2B17p=402


So we now have the system

system%2815s%2B10p=300%2C12s%2B17p=402%29


17%2815s%2B10p%29=17%28300%29 Multiply the both sides of the first equation by 17.


255s%2B170p=5100 Distribute and multiply.


-10%2812s%2B17p%29=-10%28402%29 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%28255s%2B170p=5100%2C-120s-170p=-4020%29


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


%28255s%2B170p%29%2B%28-120s-170p%29=%285100%29%2B%28-4020%29


%28255s%2B-120s%29%2B%28170p%2B-170p%29=5100%2B-4020 Group like terms.


135s%2B0p=1080 Combine like terms.


135s=1080 Simplify.


s=%281080%29%2F%28135%29 Divide both sides by 135 to isolate s.


s=8 Reduce.


------------------------------------------------------------------


255s%2B170p=5100 Now go back to the first equation.


255%288%29%2B170p=5100 Plug in s=8.


2040%2B170p=5100 Multiply.


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


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


p=%283060%29%2F%28170%29 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%2A8=200 dollars and the total cost of 40 pants is 40%2A18=720 dollars. Add this up to get 200%2B720=920 dollars.


So the total cost of 25 work shirts and 40 pairs of pants is $920. Since 920%3C950, this means that they will have enough money.