# Solving Equations with Variables on Both Sides Example

Algebra | Understand solving equations as a process of reasoning Understand solving equations as a process of reasoning and explain the reasoning |

Language | English Language |

### Transcript

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

gifts on the way to the sugar plum all acute

victim recognizes rudolph and offers to give him seven dollars

to take a photo with he and his famous knows

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

pays the vixen two dollars to take a photo with

running in his slightly less famous schnoz Well rudolph even

asked the vixen teo give the seven dollars to running

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

purchase two hats while rudolph has exactly enough to buy

one Can you determine the price of one of these

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

be able to solve this sort of problem however because

the type of situation that pops up a lot in

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

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

reindeer started with but we do know that they started

with the same amount since the problem tells us that

rudolph gave half is cash to running before they headed

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

both Then rudolph gave two dollars to the cute vixen

so ex minus two running on the other hand received

seven dollars from his fangirl So x plus seven goes

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

buy twice as many hats Is rudolph after this little

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

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

another So two times the quantity x minus two equals

x plus seven multiplying that two on the left hand

side we get to x minus four equals x plus

seven Of course we want to get x by itself

so we know how much cash all of these guys

started with so we can subtract x from both sides

to get x minus four equals seven then had four

to each side to get x equals eleven And there

we have it Each ranger started their shopping trip with

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

know that rudolph gave away two dollars and still had

exactly enough money to buy one hat itself He started

with eleven bucks and gave way to box leaving himself

with nine box Then each hat must run nine dollars

on the button We can double check to see if

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

equation We started with eleven dollars and the vixen gave

him another seven giving him eighteen dollars total And sure

enough eighteen divided by nine is too meaning Running would

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

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