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Thank you multistep equations with variables on both sides ah

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la shmoop running the reindeer has always tried to follow

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in the footsteps of his brother rudolf every year rudolph

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by santa and expensive new hat out of the goodness

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of his heart rudolph gives running exactly half his cash

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so they'll have the same amount to spend on christmas

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gifts on the way to the sugar plum all acute

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victim recognizes rudolph and offers to give him seven dollars

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to take a photo with he and his famous knows

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rudolph doesn't want running to feel left out so he

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pays the vixen two dollars to take a photo with

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running in his slightly less famous schnoz Well rudolph even

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asked the vixen teo give the seven dollars to running

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instead we'll check out running has exactly enough money to

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purchase two hats while rudolph has exactly enough to buy

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one Can you determine the price of one of these

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hats Hoof a lot of information Well it'll help to

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be able to solve this sort of problem however because

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the type of situation that pops up a lot in

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real life first we need to determine the variable we're

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going to use way don't know how much money each

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reindeer started with but we do know that they started

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with the same amount since the problem tells us that

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rudolph gave half is cash to running before they headed

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out So let's call their starting cash ex same for

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both Then rudolph gave two dollars to the cute vixen

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so ex minus two running on the other hand received

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seven dollars from his fangirl So x plus seven goes

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there However we're also told that running is able to

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buy twice as many hats Is rudolph after this little

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exchange which means that we'd have to multiply the expression

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for rudolph by two has set he's equal to one

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another So two times the quantity x minus two equals

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x plus seven multiplying that two on the left hand

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side we get to x minus four equals x plus

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seven Of course we want to get x by itself

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so we know how much cash all of these guys

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started with so we can subtract x from both sides

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to get x minus four equals seven then had four

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to each side to get x equals eleven And there

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we have it Each ranger started their shopping trip with

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eleven bucks but that's not what the questions asking We

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know that rudolph gave away two dollars and still had

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exactly enough money to buy one hat itself He started

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with eleven bucks and gave way to box leaving himself

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with nine box Then each hat must run nine dollars

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on the button We can double check to see if

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that's correct by plugging the same number in the runnings

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equation We started with eleven dollars and the vixen gave

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him another seven giving him eighteen dollars total And sure

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enough eighteen divided by nine is too meaning Running would

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have had exactly enough cash to buy two hats It's

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like santa has a new favorite this year This allergy 00:02:52.87 --> [endTime] season strikes

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