Question

paul is the elder brother of lisa. paul's age seven years ago is equal to lisa's age three years ago. the ratio between lisa's age eight years hence and paul's age two years ago is 8:5.

Answer 1

Answer:

Paul = 12 years old

Lisa = 8 years old

Step-by-step explanation:

Let Paul be x years old

Let Lisa be y years old

Paul's age 7 years ago is equal to Lisa's age 3 years ago

⇒ x - 7 = y - 3

⇒ y = x - 4

Ratio between Lisa's age 8 years later and Paul's age two years ago is 8:5.

⇒ (y + 8) / (x - 2) = 8/5

⇒ 5(y + 8) = 8(x - 2)

⇒ 5y + 40 = 8x - 16

⇒ 5y = 8x - 56

Solve x and y:

y = x - 4 ------------------------- [ 1 ]

5y = 8x - 56 ------------------- [ 2 ]

[ 1 ] x 5 :

5y = 5x - 20 ------------------- [ 1a ]

Equate [ 1a ] = [ 2 ]

5x - 20 = 8x - 56

3x = 36

x = 12

Find y:

y = x - 4

y = 12 - 4 = 8

Find their age:

Paul = x = 12 years old

Lisa = y = 8 years old

Answer: Paul is 12 years old and Lisa is 8 years old