oo yay! another trig problem!?

Question

well here is another trig qustion....i think i have the right equations but not sure....here is the question...

"A small corporation borrowed $775000to expand its product line. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest was $67000 and the amount borrowed at 8% was four times the amount borrowed at 10%?"

i have 3 equations but i dont think they are right...if they are...i must be messing up with my math...here they are...

x+y+z=775000
.08x+.09y+.1z=67000
.08x=4(.1z)

and yet again:
x=8% money
y=9% money
z=10% money

help agian would be appreciated!

NOTE:

i know everyone is saying this isn't trig...but it is in my trig book in chapter 7...weird i know...haha

Answer 1

Amanda my dear, where is the trig?

this is simple algebra.

x=8% money
y=9% money
z=10% money

x+y+z = 775000
0.08x + 0.09y + 0.1z =67000
the AMOUNT not interest is 4 times so:
x = 4z
plug in 4z for x in both equations to get:

4z+y+z = 775000
0.08(4z) + 0.09y + 0.1z =67000

5z + y = 775000
y = 775000 - 5z and
0.32z + 0.09y + 0.1z = 67000
0.42z +0.09y = 67000

Now, plug in y from the first equation into the second

0.42z + 0.09(775000 - 5z) = 67000
0.42z + 69750 - 0.45z = 67000
0.03z = 2750
z= $91,666.667

y = 775000 - 5z
y = 775000 - 5(91666.667)
y= $316,666.667

x= 4z
x= 4 (91666.667)
x= $366,666.66

Answer 2

You are on the right track.

Take a look at your third equation.

It is the amount borrowed that is four times the other amount borrowed, not the interest.

Hence, the correct third equation is x=4z.

Now, plug this value for x back into equations one and two.

That will give you two equations in two unknowns (y &z), which you can use to solve for y & z and then use those solutions to find x.

The numbers look pretty messy, so make sure you do each step explicitly on paper, skip lines between each step, do your calculations carefully, so that you leave a nice paper trail if you need to go back and check your work.

Good luck and good work on setting up the equations.

Answer 3

nicely, that isn't any longer a product y = x + cot x that's the sum of two words the spinoff is dy = a million + - csc^2(x) so dy = a million - csc^2(x) only the spinoff of 'x' , and the spinoff of (cot(x))