Dante bought a desktop computer and a laptop computer. Before finance charges, the laptop cost more than the fifferent financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year
were . How much did each computer cost before finance charges?
Note that the ALEKS graphing calculator can be used to make computations easier.

Ask by Mathis Best. in the United States

Jan 24,2025

Question

Dante bought a desktop computer and a laptop computer. Before finance charges, the laptop cost more than the fifferent financing plans. For the desktop the interest rate was per year, and for the laptop it was per year. The total finance charges for one year
were . How much did each computer cost before finance charges?
Note that the ALEKS graphing calculator can be used to make computations easier.

Ask by Mathis Best. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

Let's solve the problem step-by-step.

**Let:**
- $$ D $$ = Cost of the desktop before finance charges.
- $$ L $$ = Cost of the laptop before finance charges.

**Given:**
1. The laptop costs \$450 more than the desktop:
   $$
   L = D + 450
   $$
2. The interest rates:
   - Desktop: 9% per year
   - Laptop: 6% per year
3. Total finance charges for one year: \$300.

**Finance Charges Calculation:**
$$
\text{Finance Charges} = 0.09D + 0.06L = 300
$$

**Substitute $$ L = D + 450 $$ into the finance charges equation:**
$$
0.09D + 0.06(D + 450) = 300
$$
$$
0.09D + 0.06D + 27 = 300
$$
$$
0.15D + 27 = 300
$$
$$
0.15D = 273
$$
$$
D = \frac{273}{0.15} = 1820
$$

**Now, find $$ L $$:**
$$
L = 1820 + 450 = 2270
$$

**Verification:**
- Desktop finance charge: $$ 0.09 \times 1820 = 163.80 $$
- Laptop finance charge: $$ 0.06 \times 2270 = 136.20 $$
- Total finance charges: $$ 163.80 + 136.20 = 300 $$ (matches the given total)

**Answer:**
- **Desktop Cost:** \$1,820
- **Laptop Cost:** \$2,270
The desktop costs \$1,820 and the laptop costs \$2,270 before finance charges.

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