Interest Problems
1. Problem: Find the sales tax rate given the cost of the laptop and the sales tax amount.
Step 1: Let the sales tax rate be $r$.
Step 2: Sales tax formula: $$\text{Sales Tax} = \text{Cost} \times r$$
Step 3: Substitute values: $$2318.80 = 28985 \times r$$
Step 4: Solve for $r$:
$$r = \frac{2318.80}{28985} = 0.08$$
Step 5: Convert to percentage:
$$0.08 \times 100\% = 8\%$$
Answer: The sales tax rate is 8%.
2. Problem: Find the amount Kent borrowed given the interest, rate, and time.
Step 1: Use the simple interest formula:
$$I = P \times r \times t$$
where $I$=interest, $P$=principal, $r$=rate, $t$=time in years.
Step 2: Given $I = 45$, $r = 4\% = 0.04$, $t = 0.5$ years.
Step 3: Substitute values:
$$45 = P \times 0.04 \times 0.5$$
Step 4: Solve for $P$:
$$P = \frac{45}{0.04 \times 0.5} = \frac{45}{0.02} = 2250$$
Answer: Kent borrowed 2250.
3. Problem: Find Lea's commission given the total sales and commission rate.
Step 1: Commission formula:
$$\text{Commission} = \text{Total Sales} \times \text{Rate}$$
Step 2: Given total sales = 37000, rate = 15% = 0.15.
Step 3: Calculate commission:
$$37000 \times 0.15 = 5550$$
Answer: Lea's commission is 5550.
4. Problem: Calculate total payment Dolly needs to make after borrowing money with interest.
Step 1: Use simple interest formula:
$$I = P \times r \times t$$
Given $P=3000$, $r=3.5\% = 0.035$, $t=2$ years.
Step 2: Calculate interest:
$$I = 3000 \times 0.035 \times 2 = 210$$
Step 3: Calculate total payment:
$$\text{Total} = P + I = 3000 + 210 = 3210$$
Answer: Dolly will pay 3210 after 2 years.
5. Problem: Calculate the interest Jommel will pay.
Step 1: Given $P=1200$, $r=6.5\% = 0.065$, $t=9$ months = 9/12 = 0.75 years.
Step 2: Calculate interest:
$$I = P \times r \times t = 1200 \times 0.065 \times 0.75 = 58.5$$
Answer: Jommel will pay 58.5 as interest.