Alison is now three times as old as Jeremy, but 5 years ago, she was 5

Question

Alison is now three times as old as Jeremy, but 5 years ago, she was 5 times as old as he was. How old is Alison now?

A. 10
B. 12
C. 24
D. 30
E. 36

Ayeka · Answer

Age now, A=3J
Age 5 years ago, (A-5)=5(J-5) 
 3J-5=5J-25 
 2J=20
Jeremy’s age= 10 
Alison’s age= 3J= 3(10)= 30

Answer:D

Sajjad1994 · Answer

OE

Backsolve starting with C. If Alison is now 24, Jeremy is 8, and 5 years ago, they would have been 19 and 3, which is more than 5 times as much. Eliminate A, B, and C, and try a bigger value. If Alison is now 30, Jeremy is 10, and 5 years ago, they would have been 25 and 5. That’s it; 25 is 5 times 5.

**If Jeremy is now x, Alison is 3x, and 5 years ago they were x – 5 and 3x – 5, respectively. Now, solve:

3x – 5 = 5(x – 5) ⇒ 3x – 5 = 5x – 25 ⇒ 2x = 20 ⇒ x = 10 ⇒ 3x = 30  
 
  Answer: D

GmatKnightTutor · Answer

We can create two expressions.

i) a = 3j

ii) a - 5 = 5 (j - 5)

Based on the first expression, we can replace "a" with "3j" in the second expression.

3j - 5 = 5 (j - 5)

3j - 5 = 5j - 25

20 = 2j

10 = j

If j is 10, then a is 3(10) = 30

(D) is your answer.

Alison is now three times as old as Jeremy, but 5 years ago, she was 5

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