Question 1148351
Jill invested $100,000 in stocks and bonds. Equities earned a total return of
12%, and the fixed income component earned 8%. If she had invested twice
as much in equities, she would have made $1,800 more. How much was
invested in equities?

I don't need the answer as much as I need to understand the steps. Your help is greatly appreciated, thank you in advance!!!!
<pre>Let amount invested in equities (stocks), be E
Then amount invested in bonds = 100,000 - E
With stocks' and bonds' RORs being 12% and 8%, respectively, we get the following interest amounts: .12E and .08(100,000 - E) = 8,000 - .08E
Therefore, total earnings = .12E + 8,000 - .08E = .04E + 8,000
We then get: .12(2E) + .08(100,000 - 2E) = .04E + 8,000 + 1,800
.24E + 8,000 - .16E = .04E + 9,800
.24E - .16E - .04E = 9,800 - 8,000
.04E = 1,800
E, or {{{highlight_green(matrix(1,8, Amount, invested, in, "equities (stocks)", "=", "1,800"/.04, "=", "$45,000"))}}}