# Algebra

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An investment of ​\$54,000 was made by a business club.The investment was split into three parts and lasted for one year.The first part of the investment earned​ 8% interest, the second​ 6%, and the third​ 9%. Total interest from the investments was \$ 4260.  The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment.
x * 0.08 y* 0.09 z* 0.06 = 4260 I multiply by 100 (1)
8x+9y+6z=426,000 (1)
8x+6(9y)=0 (2)
8x+54y=0 (2)
x+y+z=54,000 (3)
.............................
8x+9y+6z=426,000 (1)
x+y+z=54,000 (3) *-6
-6x-6y-6z=-324000 (4)
........................................
8x+9y+6z=426,000 (1)
-6x-6y-6z=-324000 (4)
..................................
2x+3y=102000 (5) *-4
-8x-12y=-408000
8x+54y=0 (2)
...................................
42y=-408000
y= -68000/7 I find the y
.............................
is that correct ?

• Algebra -

how can y be negative?

x+y+z = 54000
.08x + .06y + .09z = 4260
.08x = 6*.06y

x,y,z = 36000, 8000, 10000
-----------------------------------
So, where did you go wrong?

8x+6(9y)=0

Why do you think the interest sums to zero?

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