Investment savings = 4,000 + x.
Profit Made in fund A = 5% or 200. (200 is 5% of 4,000)
Profit made in fund B = 2% or y (use to replace soon)
What is X if 200 + y = 4% --- (Translate the text "How much did she invest in Fund B, if both funds together returned a 4% profit?")
Replacing time...
What is X if 200 + 2% = 4%
What is X if 200 is = 2% (----I did 200 = 4% - 2%)
X will be 10,000
Seriously... I learned these in 6th or 7th grade.
where x = the weight of A in the portfolio and (1 - x) = the weight of B in the portfolio (weights are in decimal form)
0.05(x) + 0.02(1 - x) = 0.04
0.05x + 0.02 - 0.02x = 0.04
0.05x - 0.02x = 0.02
0.03x = 0.02
x = 0.02 / 0.03
x = 0.66667 < weight of A
(1 - x) = 0.33333
Total invested: 4,000 / 0.66667 = $6,000
Total 6,000 - amount in A 4,000 = amount in B: $2,000
Check math: 4,000(0.05) + 2,000(0.02) = 200 + 40 = 240
240 / 6000 = 0.04, or 4%
Set an equality. You know that she made .04($4,000). You know that she invested X% making 5% (.05(X) and you know that she made2% in the rest ($4,000 - X), so
.05(X) + .02($4.000 - X) = .04($4,000)
Now solve for X and $4,000 - X
Raina invested her savings in two investment funds. The $4000 that she invested in Fund A returned a 5% profit. The amount that she invested in Fund B returned a 2% profit. How much did she invest in Fund B, if both funds together returned a 4% profit?
