Let's solve each problem one by one.

Problem 1

Kim's Weekly Salary:

Kim earns a base salary of P3600 per week plus an 8% commission on sales. His total sales for the week were P22,500.

1. Calculate the commission:
   $\text{Commission} = 0.08 \times \text{Sales} = 0.08 \times 22,500 = P1,800$

2. Calculate the total weekly salary:
   $\text{Weekly Salary} = \text{Base Salary} + \text{Commission} = 3600 + 1800 = P5,400$

Kim's weekly salary is P5,400.

Problem 2

Marina's Earnings as a Real Estate Agent:

Marina sold a house for P2,500,000 with a 3% commission.

1. Calculate the commission:
   $\text{Commission} = 0.03 \times \text{Sales} = 0.03 \times 2,500,000 = P75,000$

Marina earned P75,000 from the sale of the house.

Problem 3

Commission Rate of the Sales Agent:

A sales agent received P5,800 after selling appliances worth P123,800.

1. Let $r$ be the commission rate.
   $\text{Commission Amount} = r \times \text{Sales}$

2. Set up the equation and solve for $r$:
   $5800 = r \times 123,800 \implies r = \frac{5800}{123,800} \approx 0.0468$

Convert to a percentage:
$r = 0.0468 \times 100 \approx 4.68\%$

The commission rate is approximately 4.68%.

Problem 4

Sales Tax for Carlo's Shoes:

Carlo bought a pair of shoes for P2,450 plus a 10% VAT.

1. Calculate the VAT:
   $\text{VAT} = 0.10 \times \text{Price} = 0.10 \times 2,450 = P245$

The sales tax Carlo needs to pay is P245.

Problem 5

Total Payment Including Sales Tax:

Items were bought for P12,564 plus a 12.8% sales tax.

1. Calculate the sales tax:
   $\text{Sales Tax} = 0.128 \times \text{Price} = 0.128 \times 12,564 = P1,608.19$

2. Calculate the total amount to be paid:
   $\text{Total Payment} = \text{Price} + \text{Sales Tax} = 12,564 + 1,608.19 = P14,172.19$

The total amount to be paid is P14,172.19.

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Would you like more details or have any questions about these solutions?

Related Questions:

1. If Kim's commission rate increases to 10%, what would his new weekly salary be?
2. How much would Marina make if the house was sold for P3,000,000 instead?
3. What would the sales agent's commission be if the sales amount doubled?
4. If Carlo received a 15% discount on the shoes before tax, how much would he pay including VAT?
5. If the grocery sales tax increases to 15%, how much more would be paid?

Tip:

When calculating percentages, remember to convert the percentage to a decimal by dividing by 100.