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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 = (X)(0.04)(1)
I = 0.04X

For the interest at 5% per annum
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.