Question 1203977
<pre>
Joseph invested a total of $10,000$10,000 in two accounts. After a year, one account lost 7.8%, while the other account gained 6.7%. In total, Joseph lost \$562.50. How much money did Joseph invest in each account?Write and solve a system of equations to answer the following questions.Joseph invested in the account with 7.8% loss.Joseph investedin the account with 6.7% gain.

Let amounts invested in the 7.8% and 6.7% accounts be H, and L, respectively
We then get the following INVESTMENT equation: H + L = 10,000____L = 10,000 - H ---- eq (i)

Loss "suffered" on 7.8% investment: - .078H
Gain on 6.7% account: .067L
Therefore, we get the following RETURN-ON-INVESTMENT (ROI) equation: 
                       - .078H + .067L = - 562.5 ---- eq (ii)
            - .078H + .067(10,000 - H) = - 562.5 ---- Substituting 10,000 - H for L in eq (ii)
                 - .078H + 670 - .067H = - 562.5
                       - .078H - .067H = - 562.5 - 670
                               - .145H = - 1,232.5
Amount invested in 7.8% account, or {{{highlight_green(matrix(1,7, H, "=", ("- 1,232.5")/(- .145), ", or", (" - 1,232,500")/(- 145), "=", highlight(highlight_green(highlight("$8,500")))))}}}

Obviously, amount invested in the 6.7% account, or L = $10,000 - $8,500 = $1,500.</pre>