math question

[loumeinhart 0]

Stumped on my kid's math problem.

"Tom" quoted a price of $1500 including tax (8.25%)
The client then asked that tax be visibly itemized. Tom will need to figure out his pre-tax price..

So now I'm stumped..

Price (including 8.25% tax) = $1500

I'm trying to remember the algebra on determining original amount

/?

.0825(X)=Y
X+Y=1500

/?

[stayhigh 2]

x= pre tax price. 0.0825x=tax.
x+ .0825x=1500
1.0825x=1500
x=?

or your way is correct as well. You just gotta label what x and y represents, and try to put variables on one side.

Bernie Sanders for President 2016

[loumeinhart 0]

I slept through too many classes..

Quote

x+ .0825x=1500
1.0825x=1500

how does x+.0825x translate to 1.0825x ?

[nigel99 567]

loumeinhart

I slept through too many classes..

Quote

x+ .0825x=1500
1.0825x=1500

how does x+.0825x translate to 1.0825x ?

Maybe think of it like this
(1+0.0825)x = 1500

Don't know if that helps to visualise the step?

Experienced jumper - someone who has made mistakes more often than I have and lived.

[Squeak 17]

nigel99

***I slept through too many classes..

Quote

x+ .0825x=1500
1.0825x=1500

how does x+.0825x translate to 1.0825x ?

Maybe think of it like this
(1+0.0825)x = 1500

Don't know if that helps to visualise the step?

Nigel is correct
1.0825 x X = 1500
Therefore 1500/ 1,0825 = X

1500 - X = Tax

You are not now, nor will you ever be, good enough to not die in this sport (Sparky)
My Life ROCKS!
How's yours doing?

[loumeinhart 0]

Quote

Nigel is correct
1.0825 x X = 1500
Therefore 1500/ 1,0825 = X

1500 - X = Tax

I'm more lost than db cooper's underwear..
why did we add 1 to the tax percentage?

(1+0.0825)x = 1500

?

by the way, thank you all for the help

[ghost47 18]

Quote

I'm more lost than db cooper's underwear..
why did we add 1 to the tax percentage?

(1+0.0825)x = 1500

X is the price of the item
0.0825X is the price of the tax

We know that X + 0.0825X = $1,500

X is the same as 1X (1 times anything is itself)

Therefore 1X + 0.0825X = $1,500

Or (1+0.0825)X = $1,500

Or 1.0825X = $1,500

Or X = $1,500 / 1.0825

[Glitch 0]

There is an 'understoond' 1 in front of the X that isn't normally shown.... representing (1*X). Common convention is to drop the '1'....
To follow on... (1*X) + (.0825*X) = (1+.0825)*X = 1.0825*X = 1.0825X

Clear as mud?

Randomly f'n thingies up since before I was born...

[DanG 1]

What your kid might know (but you probably don't remember) is the distributive property of multiplication.

(A + B) * C = A*C + B*C
and conversely,
A*C + B*C = (A + B) * C

or, in this case

1*Pretax-price + 0.0825*Pretax-price = 1500
therefore,
(1 + 0.0825) * Pretax-price = 1500
and finally,
Pretax-price = 1500 / (1 + 0.0825)

- Dan G

[RMK 3]

Answer is 1385.68

Yes, the elaborate old-school method works; but confuses non-math jocks.

Better to "think" about what is happening. A number with an added 8.25% is 1.0825 times of whatever that number is. Divide 1500 by 1.0825 = 1385.68

"Pain is the best instructor, but no one wants to attend his classes"

[jdkalou 0]

BINGO!!!!!!!!!!!! Man they made this much harder than it had to be!!!!!!!!!!!!

[millertime24 8]

Yep. Easiest possible way to solve this one.

Muff #5048

[champu 1]

RMK

Better to "think" about what is happening.

People's brains aren't all wired the same or to the same extent in certain topics. "Thinking" your way through an arithmetic or algebraic problem you never learned to do the old-school way is no guarantee of success.

It can certainly be helpful in remembering how to do something though.

[DanG 1]

Quote

Better to "think" about what is happening. A number with an added 8.25% is 1.0825 times of whatever that number is. Divide 1500 by 1.0825 = 1385.68

You just said the exact same thing as everyone else, but you used different words.

I fail to see how anyone was using an "elobarate, old-school method" unless you're refering to the fact that algebra is thousands of years old. No one was any more elobarate than you.

- Dan G

[RMK 3]

champu

***Better to "think" about what is happening.

People's brains aren't all wired the same or to the same extent in certain topics. "Thinking" your way through an arithmetic or algebraic problem you never learned to do the old-school way is no guarantee of success.

It can certainly be helpful in remembering how to do something though.

The simplest and most “elegant” solution is always best.

Yes, every post above mine is also a correct solution; it is just that the prior explanations could still be daunting to many. It’s not clever to dazzle with several lines of algebra when dividing two numbers into each other solves the problem.

I see you're also intelligent and have math skills, but engineers aren’t always known for their people skills. Regarding “doing it old school method”, I’m actually a Mensa member and that is no problem; but it’s not good form to “wear it on your sleeve” to impress others with how clever you are - better to answer in a manner that is most easily understood.

"Pain is the best instructor, but no one wants to attend his classes"

[mrubin 0]

I think people went into more detail because the OP was about helping his kid figure it out. Even though your post gets him the right answer, its probably more beneficial to the kid to see the process of how that final equation and answer were reached.

Just my $0.02

"I fly because it releases my mind from the tyranny of petty things." - Antoine de Saint-Exupery

[RMK 3]

The education systems have been “tinkering” with how verbal skills are taught for the past several decades. No reason Algebra has to instructed in the same manner as the 1950’s.

I think the way math is taught in schools turns many people off (which really helps no one)

"Pain is the best instructor, but no one wants to attend his classes"

[champu 1]

I find that I tend to learn/understand mathematical concepts best when I have both the symbolic representation and the relationship stated in English or as a plot/diagram. When I can go back and forth between the two, that's when I know I "get it." One form helps you get to the results, the other helps you appreciate them.

For what it's worth, I would do the problem in the OP exactly as you stated. In fact, my brain already had "1500 divided by 1.0825" queued up before I even read as far as "The client then..." But telling someone that's how you solve this problem is about as useful as when my friend took me out on a snowboarding trip for the first time and explained that the way you snowboard is, "to just go."

[jakee 1,561]

Quote

For what it's worth, I would do the problem in the OP exactly as you stated. In fact, my brain already had "1500 divided by 1.0825" queued up before I even read as far as "The client then..." But telling someone that's how you solve this problem is about as useful as when my friend took me out on a snowboarding trip for the first time and explained that the way you snowboard is, "to just go."

Which is why I would say "So - you have 108.25% of the pretax value. Divide it by 108.25 to get 1% of the value. Times that by 100 to get 100% of the pretax value." And you can write down the math while you're explaining it verbally.

Then, if they're any good with processes they'll soon figure out that they can get there in one step instead of two. And if they're not, there's always the arts

Do you want to have an ideagasm?

[stayhigh 2]

Meth question of the day.

You have pile of 95% pure cocaine, and you also have a pile of 55% pure cocaine.

How much of each amount of cocaine is needed to make 1000 grams of 75% pure mixture of cocaine?

Bernie Sanders for President 2016

[muff528 3]

500 grams of each.

[loumeinhart 0]

got it, thanks for the help guys. I did completely forget about the distributive property. And that x= 1x

[rehmwa 2]

New Math -

Tom is trying to sell something to his client for $1500 (including tax).
Neither the client, nor Tom can calculate the amount of tax contained in the price.

"Math" Questions:

1 (10%) - how does the funding of the national education system fail the average shop owner and customer

2 (10%) - Is Tom a horrible business exploiter of helpless poor consumers? Or is the client a wealthy rapist of the environment since he can afford something this expensive? (points added for each 'yes' answer).

3 (20%) - How does the normal person that can't afford $1500 items feel when watching Tom sell expensive products to rich clients?

4 (5%) - Draft a price control proposal that requires Tom to sell these same items to people with less money for a price well under Tom's cost.

5 (5%) - Explain the best way to issue the proposal that doesn't require paper or oil to be consumed by society.

6 (50%) - Return signoff that parents have receive NEA discussion of yearly property tax increase for funding for local school administration charges.

...
Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants

[kallend 2,106]

As a physics and engineering prof., it really bugs me that we have freshmen entering with good scores in AP Calculus who'd have a hard time with that question.

IMNSHO, the schools would be better off teaching problem solving skills, algebra, geometry and trig than emphasizing rote methods of doing arithmetic (invented so Bob Cratchett could clerk for Ebeneezer Scrooge) and then pushing kids into calculus before they really understand algebra and trig.

...

The only sure way to survive a canopy collision is not to have one.

[BillyVance 34]

I was good at algebra and trig in high school. But for the life of me, could not understand calculus.

My brother was a whiz though. Valedictorian of his small college prep private school, where he aced Calculus II as a senior.

"Mediocre people don't like high achievers, and high achievers don't like mediocre people." - SIX TIME National Champion coach Nick Saban