Greg is 18 years older than his sister Gloria. In 6 years, he will be twice as old as Gloria. How old is each of them now?

Question

Genesis Allen · Accepted Answer

Greg is 30 and Gloria is 12

Let's call Greg's age now #g#. And, Let's call Gloria's age now #r#. Given that Gloria is now eighteen years older than Greg, we can write: #g = r + 18# We also know in 6 years (#g + 6)# he will be twice as old as Gloria. So we can write: #g + 6 = 2(r + 6)# From the first equation we can substitute #r + 18# for #g# in the second equation and solve for #r#: #(r + 18) + 6 = 2(r + 6)# #r + 18 + 6 = 2r + 12# #r + 24 = 2r + 12# #r - r + 24 - 12 = 2r +12 - r - 12# #24 - 12 = r# #r = 12# Now that we know Gloria is 12 we can calculate Greg's age by substituting #12# for #r# in the first equation and calculating #g#: #g = 12 + 18# #g = 30#

Hazel Anglin · Answer

undefined Let's denote Greg's age as $ G $ and Gloria's age as $ G $.

According to the given information, we can form two equations:

1. $ G = G + 18 $  (Greg is 18 years older than Gloria)
2. $ G + 6 = 2(G + 6) $  (In 6 years, Greg will be twice as old as Gloria)

From equation 1, we can deduce that $ G = G + 18 - 18 = G $. This indicates that Greg and Gloria are the same age, which is impossible given the context.

This suggests that there might be a mistake in the problem statement or that it lacks sufficient information to solve it.