[Maaso]

This chapter is titled: "Problems involving percent"

The sample problem here is....You have a total of $8000 invested in two simple interest accounts. On one account; a money market fund, and annual simple interest rate is 11.5%. On the second account; a bond fund, the annual simple interest rate is 9.75%. The total annual interest earned by the two accounts is $823.75. How much have you invested in each account?

In the book they have a little chart I will try to draw:

Principal Interest Interest earned
Amount @ 11.5% | x | 0.115 | .115x
Amount @ 9.75% |8000 - x | 0.0975 | .0975(8000-x)

Then the equation below it is:

.115x+.0975(8000-x) = 823.75
.115x + 780 -.0975 = 823.75 (This I understand, multiply to get rid of the parenthesis)
.0175x + 780 = 823.75 (Subtract from each side; .110 - .0975 = .0175)
0.175x = 43.75 (subtract the whole numbers; 823.75 - 780 = 43.75)
x = 2500

The amount invested at 9.75% is 8000 - x
Replace x with 2500 and evaluate.
8000 - x = 8000 - 2500 =5500

The amount invested at 11.5% = $2500
The amount invested at 9.75% = $5500


That lest step in the equation is where I get lost....where the fuck did that 2500 come from? Did they just guess? I just don't get it.

 

[Strangerous]

$8,000 - $5,500 = $2,500

It's logical to me!

 

[Maaso]

$8,000 - $5,500 = $2,500

It's logical to me!

Only because it explains the answer at the end, but how they got the answer is beyond me.

I figured it out though, went and scheduled me a tutor during my lunch period. Apparently you divide the 43.75 by .175 and it somehow equals 2500.

 

[gtv]

Maaso, you have shifted a decimal point.

Step 1: .115x+.0975(8000-x) = 823.75
Step 2: .115x + 780 -.0975x = 823.75 (This I understand, multiply to get rid of the parenthesis)
Step 3: .0175x + 780 = 823.75 (Subtract from each side; .110 - .0975 = .0175)
Step 4: 0.175x = 43.75 (subtract the whole numbers; 823.75 - 780 = 43.75)
Step 5: x = 2500

When you go from Step 2 to Step 3, you have the correct value of 0.0175x, but somehow in Step 4, you now have it as 0.175x. 43.75 / 0.175 is equal to 250, but 43.75 / 0.0175 is equal to 2500.

 

[condition1]

I don't know, but if you don't get off Train A it will eventually crash with Train B!

 

[NDS]

I don't know, but if you don't get off Train A it will eventually crash with Train B!

Just for you, since you're such a fan of train travel:

if a train is travelling at 22mph, and a car is travelling at 89mph, how long will it be until the car catches up with the train if the train left 4 hrs before the car did?

 

[Strangerous]

Answer
Assuming they both leave from the same point, and travel the same path, the car will catch up with the train when:

Distance travelled by car = distance travelled by the train

(Speed of car)(time of car) = (speed of train)(time of train)

speed of car = 89mph
speed of train = 22mph
let time of train = t
then time of car = t-4

So your job to find time (t) which satisfies the equation:

(89)(t-4) = 22t

 

[NDS]

http://en.allexperts.com/q/Word-Problems-2062/math-37.htm

Answer
Assuming they both leave from the same point, and travel the same path, the car will catch up with the train when:

Distance travelled by car = distance travelled by the train

(Speed of car)(time of car) = (speed of train)(time of train)

speed of car = 89mph
speed of train = 22mph
let time of train = t
then time of car = t-4

So your job to find time (t) which satisfies the equation:

(89)(t-4) = 22t

You could have let him google it for himself..

 

[Strangerous]

He still has to solve it!

 

[Silicon Wolverine]

now i know why i nearly failed algebra. and never even tried geometry.

SW

 

[Mstr33t]

I think my brain exploded trying to read the equations...

 

[godlessdustin]

I hated algebra but I loved geometry.

 

[Mstr33t]

I hated algebra but I loved geometry.

This is how I feel about geometry,

 

[47_MasoN_47]

This stuff sucks. I still don't understand how I'll ever need anything like this...ever.

Here's what the stuff I'm doing in Quantitative Methods 295 looks like

?14x + ?15y
------------ ------------------
x^2-x-12 x^2+x-6

When will I ever need to know how to do that? Why?

Math is gay.

 

[ajole]

When will I ever need to know how to do that? Why?

When they ask you to vote on the bailouts, the Obama medical bill, or the budget...
which explains why our politicians FAIL so badly....

 

[47_MasoN_47]

How the crap does that stuff I posted above help me any when elections come around?

EDIT: I mean what does that problem even solve?

 

[ajole]

Oh, it isn't that problem, it's the math needed to do the problem. If the politicians could do it, they'd be less likely to vote for crap that won't work, and costs too much.

That problem looks like straight algebra to me, it doesn't solve anything, it is just an exercise in DOING algebra. Can you do the correct thing at the correct time, order of operations, substitution, and so forth. My guess is you are supposed to get Y by itself, and graph the resulting line or curve? The area under the curve might mean something?

 

[47_MasoN_47]

I really have no idea. I'm just going to go to the professor and ask for mercy. It'll be my last semester if I pass these classes...finally I'll be free from the wretched grasp of college. I've already failed this one once and I'll just fail it again if he won't help me through it.

 

[ajole]

Well....factor the trinomials under the fraction bar,
X^2-X-12 is then (x-4) (x+3) and the other one is (x+3) (x-2)

then multiply each side by the denominator of the other to get rid of the fractions.

Distribute the top values across the parens, then FOIL, combine like terms and you'll be close to done...

And I could be just making it worse, since I don't know what you are trying to do... :grinwink:

Sorry, I can't really teach it to you this way. Probably should go see your professor... :yes:

I always tell my students, as you learn algebra, it is about the process, not the answer. Just do the steps. After you get good at it, you can start seeing things and it becomes easier.

 

[NDS]

You're not a woman so you've got no excuse.