Answer:
Adele's current age is 12
Step-by-step explanation:
Let a = Adele's current age
Let t = Timothy's current age
Adele is 5 years older than Timothy:
a = t + 5 {equation 1}
In 3 years Timothy will be 2/3 of Adele's age:
(2/3)(a + 3) = t + 3 {equation 2}
Since we are looking for Adele's age, let's rearrange equation 1 to:
t = a - 5
Substitute that into equation 2 and solve for a.
(2/3)(a+3) = a - 5 + 3
(2/3)(a + 3) = a - 2
Multiply through by 3 to clear the fraction
2(a+3) = 3a - 6
2a + 6 = 3a - 6
Add 6 to both sides, subtract 2a from both sides
12 = a
Adele is 12 years old
This means Timothy is 7 years old.
Check equation 2 to verify:
(2/3)(a + 3) = t + 3
(2/3)(12+3) = 7 + 3
(2/3)(15) = 10
10 = 10
