This is an example of interest problems.

We can use the formula I = PRT where, I is the interest, P principal amount or investment, R is the rate and T is the time.

We will let X as Gemma's investment at 4% interest rate per annum.

I = PRT

I = (X)(0.04)(1)

I = 0.04X

For the interest at 5% per annum

I = PRT

I = (250,000 - X)(0.05)(1)

I = 12,500 - 0.05X

Gemma received 11,500 interest from both investment

Interest at 4% + Interest at 5% = 11,500

0.04X + 12,500 - 0.05X = 11,500

- 0.01X = -1,000

X = 100,000

Therefore, Gemma's investment at 4% interest rate is P100,000 and her investment at 5% interest rate is P150,000.