#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

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

#2

pi

#3

try a system of equations maybe? i'm not sure

#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

EDIT: it has something to do with substitution. solve for x in one equasion and put it into the other and solve for y

#5

Everything is aight except it would be 0.085 and 0.075, not 0.0085

#6

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

#7

0.0085?

Wouldn't that be .85%?

EDIT: Beaten, again.

Wouldn't that be .85%?

EDIT: Beaten, again.

#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

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...

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?

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

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

?

then add like terms and find?

#12

y=2000

x=4000

just substitute its easy

x=4000

just substitute its easy

#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...

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...

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...

#15

Thanks guys! I got it done

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

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

#16

$3000 each.

#17

Thanks guys! I got it done

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

What did your answer come out to?

#18

^, yeah, tha's what I got as well, x=3000, y=3000. It checks out, as (.075 * 3000) + (.085 * 3000)=480

#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

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.

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.

#21

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

#22

ok, this sounds really stupid,

where is the $480 coming from

450 -0.075y + 0.085y = 480

where is the $480 coming from

450 -0.075y + 0.085y = 480

#23

I know this has to be simple, thats the reason why its making me crazy. Someone hurry up and answer this.