Richard is 6 years older than Lisa, and in 5 years the sum of their ages will be twice as much as the sum of their ages 4 years ago. Find their present ages.

Question

Bosnian · Answer

R = L + 6

R + 5 + L + 5 = 2 ( R - 4 + L - 4 )

R + L + 10 = 2 ( R + L - 8 )

R + L + 10 = 2 * R + 2 * L - 2 * 8

R + L + 10 = 2 R + 2 L - 16

Replace R = L + 6 in this equation

L + 6 + L + 10 = 2 ( L + 6 ) + 2 L - 16

2 L + 16 = 2 * L + 2 * 6 + 2 L - 16

2 L + 16 = 2 L + 12 + 2 L - 16

2 L + 16 = 4 L - 4 Add 4 to both sides

2 L + 16 + 4= 4 L - 4 + 4

2 L + 20 = 4 L Subtract 2 L to both sides

2 L + 20 - 2 L = 4 L - 2 L

20 = 2 L Divide both sides by 2

10 = L

L = 10 yrs

R = L + 6 = 10 + 6 = 16 yrs