#1
Hey I've got this sheet on linear equations due tommorow and I'm stuck on this one. any help is appreciated.

The Student Council invested $6000, part at 7.5% per annum and the remainder at 8.5% per annum. The total intrest, after one year, from these investments was $480. How much was invested at each rate?

This is what i have so far:
Let x represent the amount invested at 7.5%
Let y represent the amount invested at 8.5%

x+y=$6000

x(0.0075)+y(0.0085)=$480
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#4
wait.. i have no clue

EDIT: it has something to do with substitution. solve for x in one equasion and put it into the other and solve for y
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#5
Everything is aight except it would be 0.085 and 0.075, not 0.0085
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#6
Quote by BHC zoley
Hey I've got this sheet on linear equations due tommorow and I'm stuck on this one. any help is appreciated.

The Student Council invested $6000, part at 7.5% per annum and the remainder at 8.5% per annum. The total intrest, after one year, from these investments was $480. How much was invested at each rate?

This is what i have so far:
Let x represent the amount invested at 7.5%
Let y represent the amount invested at 8.5%

x+y=$6000

x(0.075)+y(0.085)=$480


x=(6000-y) now replace x down here...

(6000-y)(0.0075)+y(0.0085)=480

now solve for y
#8
A=P (1+i)^n A is the total sum. P is the payment (480 and then just add 1 to your interest. also n is the number of times you compound which i believe is one, now all you have to do is rearrange the equation to suit your question
#9
yea its a system of equations
i'm doing the same thing right now, but with three variables
tough stuff

but just graph it and see where they intersect
i think that'll work

or use substitution or elimination to figure it
#10
cant you just make x=(6000 - y) or y=(6000 - x) ? then plug on of those into your last equation and solve. So: x(0.0075)+(6000 - x)(0.0085)=$480 solve for x. when you know x, solve for y using the equation x+y= 6000. I haven't done this in a while but that should work...

EDIT: my bad, someone beat me to it. oh well...
#11
x(0.0075)+y(0.0085)=$480

y(o.oo85)=$480-x(0.0075)

therefore x(0.0075)+($480-x(0.0075))=$480

?
then add like terms and find?
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#12
y=2000
x=4000

just substitute its easy
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#13
since i have nothing better to do...

to solve a linear equation, solve for a variable:

x+y=$6000
x=$6000-y

then plug in:

(6000-y)(0.075)+y(0.085)=$480

distribute the first y:

6000*.075 - .075y + .085y = 480

combine the y's/simplify:

.01y = 480 - 450

then solve for y:

y = $3000

plug in for y:

x+y=$6000

x+3000=6000

x=3000

plugin to check (it's right) then there you go...
#14
^I'm too lazy to check whether or not this is correct.


x+y = 6000
.075x+.085y=480 Multiply this part by -40/3 to get the x's to cancel out

x+y=6000
-x-(17/15)y = -6400 Add the two equations

-(2/15)y = -400

Then y = 3000, and x=3000

Seems odd they come out the same...
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#15
Thanks guys! I got it done

Ps: Seth Cohen I have no idea what you just said
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#17
Quote by BHC zoley
Thanks guys! I got it done

Ps: Seth Cohen I have no idea what you just said


What did your answer come out to?
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#18
^, yeah, tha's what I got as well, x=3000, y=3000. It checks out, as (.075 * 3000) + (.085 * 3000)=480
Originally posted by Capua47:

Oh well if your from austrailia then grades shudn't matter considering your just gonna grow up to be ol' stevie erwin eh?!


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#19
x+y=6000
x=6000-y

0.075x + 0.085y = 480
0.075(6000-y) + 0.085y = 480
450 -0.075y + 0.085y = 480
y=3000

x = 6000 - y
x = 6000 - 3000
x = 3000

there ya go
#20
Sole the x+y=6000 equation for x, giving you x=6000-y

Then substitute in that value for x, being (6000-y), into the x value for the other equation, giving you (6,000-y)(0.075) + (0.085)y = 480

Then solve the equation for y, giving you your y value. Then you use your y value to find x, using the x+y = 6000 equation.

Note - Your percent to decimals are off - 7.5% = 0.075 10% = 0.01

EDIT: Wow, the math nerds at UG are out in force tonight.
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#21
Quote by ValvetronixRox
x+y=6000
x=6000-y

0.075x + 0.085y = 480
0.075(6000-y) + 0.085y = 480
450 -0.075y + 0.085y = 480
y=3000

x = 6000 - y
x = 6000 - 3000
x = 3000

there ya go

Where did you get this 450 from?
EDIT: Nevermind stupid me forgot to multiply i got 3000 I'm good thanks guys
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#22
ok, this sounds really stupid,

where is the $480 coming from

450 -0.075y + 0.085y = 480
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can you fuсk it?

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#23
I know this has to be simple, thats the reason why its making me crazy. Someone hurry up and answer this.
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Quote by Chordzzz
can you fuсk it?

Quote by nebiru
Oh I will find a way.