8.Mary invested RM3000 in two accounts, some at 12% per annum and the rest at 8 percent per annum.Her total interest for one year was RM3200.how much was invested at each rate?

9.RM 1999 was invested for a certain period. The simple interest earned was RM200. find the period if the simple interest rate offered was 10% per annum

8. amount invested at 12% -- x

amount invested at 8% --- 3000-x

.12x + .08(3000-x) = 3200
times 100
12x + 8(3000-x) = 320000
4x = 29600
x = ??? (more than she invested!!!!)
I think you have a typo, should the interest be RM 320 ??
That way it works out nicely,
change the 3200 to 320 and repeat my calculations

9.
I = PRT
200 = 1999(.10)T
T = 200/((.1)(1999)) = 1

One year

To solve these types of problems, we can use algebraic equations.

Let's start with question 8:

1. Assign variables: Let's say Mary invested RMx at 12% and RM(3000 - x) at 8%.

2. Write the equation for the total interest: The interest earned from the 12% investment plus the interest earned from the 8% investment should add up to RM3200.
Therefore: 0.12x + 0.08(3000 - x) = 3200.

3. Solve the equation:
Distribute the 0.08: 0.12x + 240 - 0.08x = 3200.
Combine like terms: 0.04x + 240 = 3200.
Subtract 240 from both sides: 0.04x = 2960.
Divide both sides by 0.04: x = 2960 / 0.04.
Calculate: x ≈ 74000.

4. Calculate the remaining amount: 3000 - x = 3000 - 74000 = 226000.

Therefore, Mary invested approximately RM74000 at 12% and RM226000 at 8%.

Now let's move on to question 9:

1. Assign variables: Let's say the period invested is t years.

2. Write the equation for the simple interest: The simple interest earned can be calculated using the formula I = P * r * t, where I is the simple interest, P is the principal amount, r is the interest rate, and t is the time period.
Here, we know that I = RM200, P = RM1999, and r = 10% or 0.1.
Therefore: 200 = 1999 * 0.1 * t.

3. Solve the equation:
Divide both sides by 1999 * 0.1: t = 200 / (1999 * 0.1).
Calculate: t ≈ 0.10 years.

Therefore, the period invested is approximately 0.10 years.