Carmen bought a desktop computer and a laptop computer. Before finance charges, the laptop cost \$200 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was $5 \%$ per year, and for the laptop it was $7 \%$ per year. The total finance charges for one year were $\$ 250$. How much did each computer cost before finance charges? Note that the ALEKS graphing calculator can be used to make computations easier. Desktop: $\$ \square$ Laptop: $\$ \square$

Step 1 ：Let's denote the cost of the desktop computer as D and the cost of the laptop as L.

Step 2 ：From the problem, we know that the laptop cost $200 less than the desktop. So we can write this as: \(L = D - 200\)

Step 3 ：We also know that the total finance charges for one year were $250. The finance charge for the desktop was 5% of its cost and for the laptop it was 7% of its cost. So we can write this as: \(0.05D + 0.07L = 250\)

Step 4 ：Now we can substitute \(L = D - 200\) into \(0.05D + 0.07L = 250\):

Step 5 ：Solving the equation \(0.05D + 0.07(D - 200) = 250\) gives us \(0.05D + 0.07D - 14 = 250\)

Step 6 ：Solving the equation \(0.12D = 264\) gives us \(D = 264 / 0.12\)

Step 7 ：Solving the equation \(D = 264 / 0.12\) gives us \(D = $2200\)

Step 8 ：Substitute \(D = $2200\) into \(L = D - 200\):

Step 9 ：Solving the equation \(L = 2200 - 200\) gives us \(L = $2000\)

Step 10 ：So, the desktop computer cost \(\boxed{$2200}\) and the laptop cost \(\boxed{$2000}\) before finance charges.