Answer
The investment at -4% is $3700
The investest made at +6% is $5300
Explanation:
Given
The total amount of the two investments = $9000
She lost 4% on one and gained 6% on the other
Let x represents the first investment
Let y represents the second investment
Since the two investments make a total of $9000
This can be expressed mathematically as
x + y = 9000 ---------------- equation 1
If she lost 4% on one of the investments and earned 6% in the other investment
Then this can be expressed as
-0.04x + 0.06y = 170
-0.04x + 0.06y = 170 ---------- equation 2
These two systems of the linear equation can be solved simultaneously
x + y = 9000 ------------- equation 1
-0.04xx + 0.06y = 170 ---- equation 2
We will be using the substitution method to solve the above equations
Make the x the subject of the formula in equation 1
x = 9000 - y
Substitute the value of x into equation 2
-0.04(9000 - y) + 0.06y = 170
Open the parentheses
-360 + 0.04y + 0.06y = 170
Collect the like terms
0.04y + 0.06y = 170 + 360
0.1 y = 530
Divide both sides by 0.1
y = 530 / 0.1
y = $5300
From equation 1
x + y = 9000
y = $5300
x = 9000 - y
x = 9000 - 5300
x = $3700