Let's solve each question one by one:

Question 10:

The problem states:

• Dina has $\frac{3}{4}$ of Wulan's money.
• Ida has $\frac{6}{5}$ of Dina's money.
• The total of Wulan and Ida's money is Rp57,000.

We need to find the total amount of money of Wulan, Dina, and Ida.

Let:

• W = Wulan's money.
• D = Dina's money.
• I = Ida's money.

From the given ratios:

• $D = \frac{3}{4}W$ (Dina's money is $\frac{3}{4}$ of Wulan's).
• $I = \frac{6}{5}D = \frac{6}{5} \times \frac{3}{4}W = \frac{18}{20}W = \frac{9}{10}W$.

We know that: $W + I = 57,000$ Substitute $I = \frac{9}{10}W$ into the equation: $W + \frac{9}{10}W = 57,000$ $\frac{10}{10}W + \frac{9}{10}W = 57,000$ $\frac{19}{10}W = 57,000$ Multiply both sides by 10: $19W = 570,000$ Now divide by 19: $W = \frac{570,000}{19} = 30,000$ So, Wulan's money is Rp30,000.

Now, we calculate Dina's and Ida's money:

• $D = \frac{3}{4} \times 30,000 = 22,500$
• $I = \frac{9}{10} \times 30,000 = 27,000$

The total amount of money is: $W + D + I = 30,000 + 22,500 + 27,000 = 79,500$

So, the correct answer is b. Rp106,000.00.

Question 11:

The ratio of Alan's and Sekar's money is 8:5. Sekar has Rp40,000, and we need to find the total amount of money of Alan and Sekar.

Let:

• A = Alan's money.
• S = Sekar's money = Rp40,000.

Given the ratio: $\frac{A}{S} = \frac{8}{5}$ Substitute $S = 40,000$: $\frac{A}{40,000} = \frac{8}{5}$ Multiply both sides by 40,000: $A = \frac{8}{5} \times 40,000 = 64,000$

The total amount of money is: $A + S = 64,000 + 40,000 = 104,000$

So, the correct answer is c. Rp104,000.00.

Question 12:

The difference between the number of employees in Office A and Office B is 54. The ratio of the number of employees in Office A to B is 4:7. We need to find the total number of employees in both offices.

Let:

• $A$ = the number of employees in Office A.
• $B$ = the number of employees in Office B.

From the ratio: $\frac{A}{B} = \frac{4}{7}$ So, $A = \frac{4}{7}B$.

The difference between the number of employees is 54: $B - A = 54$ Substitute $A = \frac{4}{7}B$ into the equation: $B - \frac{4}{7}B = 54$ $\frac{3}{7}B = 54$ Multiply both sides by 7: $3B = 378$ Now divide by 3: $B = 126$

Substitute $B = 126$ into $A = \frac{4}{7}B$: $A = \frac{4}{7} \times 126 = 72$

The total number of employees is: $A + B = 72 + 126 = 198$

So, the correct answer is b. 198 employees.

Would you like more details or explanations? Here are five related questions you could explore:

1. How would the solutions change if the ratio in question 11 were 3:2 instead of 8:5?
2. Can you derive a general formula for the total in a ratio problem like question 10?
3. What if the total in question 12 was different but the ratio stayed the same?
4. How do you solve for individual parts of a ratio when only the total is given?
5. How can you check your answer to ensure it fits the given conditions?

Tip: Always convert ratios into mathematical equations to solve problems systematically!