Let's say the loan is for T years at simple interest.
Let x=the amount subject to 7% interest, so the remaining part is 15000-x.
The interest after time T is 1500=0.07Tx+(15000-x)0.15T=2250T-0.08Tx.
From this, 0.08Tx=2250T-1500, so x=(2250T-1500)/(0.08T)=28125-18750/T.
If T=1, x=9375; if T>1, x would exceed 15000, therefore assume T=1, then x=9375 (subject to 7%) and 5625 subject to 15%. (28125-18750/T<15000, so 28125T-18750<15000T, 13125T<18750, T<10/7; and 28125-18750/T>0, so 28125T-18750>0 and T>18750/28125, T>2/3. This tells us that T must be between 2/3 and 10/7. T=1 is within this range.)