Proportions

[terse summit]

Anyone know how to solve this?

[pure spindle]

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[wet nova]

clear the fractions, multiply both sides by the LCM of the denominators (2,8)

[terse summit]

so 2 times 8?

or cross multiply

if i cross multiply it would be 8x = x+12

[wet nova]

well the lcm of 2,8 is actually 8

cross multiplication will also work, but you didn't quite do it right

[terse summit]

how come?

[wet nova]

what's 2(x+6)

[terse summit]

6 turns into 12

and x is 2x?

i’m guessing

[wet nova]

yeah

[terse summit]

then you add them

and u get 8

[wet nova]

your previous equation was 8x = x + 12
you updated that to 8x = 2x + 12

[terse summit]

yes sorry

so I do inverse operation on the 2x to cancel it out

so 8x divided by 2x

which is 4x

[wet nova]

no

(8x)/(2x) is not 4x
and don't divide, try to isolate x
move all the x's to the left side

[terse summit]

I add it?

ohh

so I add 2x with 8x

10x

[wet nova]

no

[terse summit]

subtract

Cus it’s adding

inverse operation of that is subtraction

[wet nova]

yes

[terse summit]

so then 6x = 12

the answer is 2

[wet nova]

yes and you can confirm by plugging it back in

[terse summit]

okay let me try it

one second

it works

may I ask one more question if you don’t mind?

[wet nova]

yes

[terse summit]

number 12

[wet nova]

what progress do you have

[terse summit]

Nothing, I don’t even know where to start

[wet nova]

say the school buys H pounds of hamburger and S pounds of soy

it gives you 2 equations

aka 2 facts

[terse summit]

okay

every hamburger is 1.50

and every soy is 1.00

[wet nova]

the total cost (350) is equal to the cost of hamburgers + the cost of soy

[terse summit]

so then 350 divided by 1

no 350 divided by 1.50

and then minus 50?

nope that doesn’t work

[wet nova]

what's the cost of hamburgers

based on the fact that you have H pounds and each pound costs 1.5

[terse summit]

right

so then 1.5 times 350??

[wet nova]

no

it's 1.5*H

[terse summit]

yes your right

then for soy its 1*H

[wet nova]

how many pounds of soy do you have

[terse summit]

uh

[wet nova]

read

[terse summit]

1*S

[wet nova]

yes right

so now make an equation from "350 = cost of hamburger + cost of soy"

[terse summit]

350 = 1.50h + 1s

[wet nova]

correct

then they also give you another fact

can you find it

[terse summit]

yes

they use 50 more pounds of soy

than hamburgers

[wet nova]

yes, so make another equation from that

[terse summit]

350 = 1.50h + 1s - 50

[wet nova]

no don't modify the first equation

new equation

[terse summit]

oh

350 - 50

[wet nova]

no this one does not involve the 350

only relates amount of hamburgers to amount of soy

[terse summit]

1*50?

[wet nova]

lets rephrase the fact
"the pounds of soy is 50 more than the pounds of hamburgers"

[terse summit]

50s + H

[wet nova]

nope

that's not an equation even

[terse summit]

i cant make an equation

adly

[wet nova]

the word "is" means equals

[terse summit]

s = 50+H

[wet nova]

yes

exactly

now you know these things:
s = 50 + h
350 = 1.5h + s

do you know how to solve that

[terse summit]

oh

so

s = 50 + h

over

350 = 1.5h + s

correct or are they seperate?

[wet nova]

idk what you mean

[terse summit]

okay nevermind

lets solve 350 = 1.5h + s first

350 = 1.5h + s

1.5h divided by 350

[wet nova]

since you are trying to find s, i would recommend solving s = 50 + h first

for h

isolate h

[terse summit]

okay bet

s = 50 + h

subract h

so we can get rid of that

then we have s = 50

[wet nova]

no

that would imply that h = 0

that doesn't make sense

also, don't subtract h, subtract 50

[terse summit]

how do you subtract from a variable

[wet nova]

you subtract 50 from both sides

[terse summit]

s = 50 + h

you subtract 50 from s

and get -50s

.

[wet nova]

no

that's multilpication

[terse summit]

im confused bro

I dont know how to solve that

[wet nova]

s = 50 + h
put -50 at the end of both sides
s - 50 = 50 + h - 50
s - 50 = h

[terse summit]

s = h + 50

[wet nova]

ok, now you know that (h), wherever you see it, is equal to (s-50)
that includes in the first equation
so you can replace it, and not change anything:
350 = 1.5h + s
this becomes
350 = 1.5(h) + s
350 = 1.5(s-50) + s

*don't forget the parentheses

[terse summit]

so i solve this

350 = 1.5(s-50) + s

[wet nova]

yeah

[terse summit]

1.5 times s

1.5s

and then 1.5 times 50

75

350 = (1.5s - 75) + s

isolate

no parenthesis first

nevermind

1.5s minus s

im lost and stuck here

[wet nova]

350 = 1.5s - 75 + s

[terse summit]

okay

[wet nova]

the parentheses weren't doing anything

[terse summit]

I add 75 to 350

425 = 1.5s + s

cancel out the s

425 divided by 1.5

[wet nova]

no

not yet

no divide

[terse summit]

okay

[wet nova]

combine like terms

[terse summit]

s = 1

so 2.5s

then divide

anser is 170

answer

let me plug it in

its correct

[wet nova]

yep

gj

[terse summit]

that wasmt so hard

I guess I just overthink things

last and final question

[wet nova]

it surprises me that you do systems of 2 equations at the same time as learning single equations

[terse summit]

exactly

number 17

this is the most confusing one yet actuslly

[wet nova]

just pretend p, and w are numbers

solve normally

for q

[terse summit]

hold on

[terse summit]

@wet nova

i’m back sorry

An antique car was purchased for $7400 and is now worth $10,600. What is the approximate percent of change?

[wet nova]

didn't you say that was the last one

percent of change is (if increasing): (new/old) - 1
if decreasing: 1 - (new/old)

[terse summit]

oh yea I just wrote that there to look at it

those are easy

it’s 43.24%

anyways back to topic

number 17

[wet nova]

so how do you isolate q

[terse summit]

I don’t know

I’ve never done equations like this before

This is like a review for a chapter test we are taking tommorow

[wet nova]

q is on the right side, but so is w

you want w to not be on the same side

so subtract it

[terse summit]

wait hold on before we do this question

I’m a bit confused on this one as it Just came to my mind.

it’s asking

The sum of a number and -16 is 25

what is the number?

i’m guessing I would set it up as 25 = -16 + x

@wet nova

[wet nova]

yes

[terse summit]

How would I solve it then tho?

so let’s cancel out the x

so now that that’s gone we have 25 = -16

correct?

[wet nova]

no

you need to remember, when you do something to one side, you have to do the same thing to the other side

25 is obviously not -16

[terse summit]

hmm

25 = -16 + x

let’s do -16 first

so 25 minus 16?

or plus

[wet nova]

which do you think

[terse summit]

minus

[wet nova]

don't guess, use the equation

[terse summit]

subtraction because it’s adding with x

inverse operation

[wet nova]

x is being added to -16

would it help if you reorder the right side to be x - 16

[terse summit]

yes actually

25 = x - 16

41

[wet nova]

yes

[terse summit]

is the a deer

yes

that wasn’t hard 😭

[wet nova]

was it not

if you see that on a test will you get it right

[terse summit]

A scale drawing of a room has a scale 1.75 inches = 1.5 feet

how long is a couch that is 7 inches

[wet nova]

how many multiples of the scale is that