adele is 5 years older than timothy. in three years, timothy will be $\frac{2}{3}$ of adeles age. what is…

Explanation:

Step1: Define variables

Let Adele's current age be $A$ and Timothy's current age be $T$. We know that $A=T + 5$.

Step2: Express ages in three - years

In three years, Adele's age will be $A + 3$ and Timothy's age will be $T+3$. And we are given that $T + 3=\frac{2}{3}(A + 3)$.

Step3: Substitute $T=A - 5$ into the second equation

Substitute $T$ in the second equation: $(A - 5)+3=\frac{2}{3}(A + 3)$. Simplify the left - hand side: $A-2=\frac{2}{3}(A + 3)$.

Step4: Expand the right - hand side

Expand $\frac{2}{3}(A + 3)$ to get $\frac{2}{3}A+2$. So the equation becomes $A - 2=\frac{2}{3}A+2$.

Step5: Solve for $A$

Subtract $\frac{2}{3}A$ from both sides: $A-\frac{2}{3}A-2=\frac{2}{3}A-\frac{2}{3}A + 2$, which simplifies to $\frac{1}{3}A-2=2$. Add 2 to both sides: $\frac{1}{3}A-2 + 2=2 + 2$, so $\frac{1}{3}A=4$. Multiply both sides by 3 to get $A = 12$.

Answer:

12