SOLUTION: ELEVEN YEARS AGO HYE WAS FOUR TIMES AS OLD AS HER BROTHER. IN 1 YEAR SHE WILL BE TWICE AS OLD AS HE IS NOW. WHAT ARE THEIR AGES?

Question 27880: ELEVEN YEARS AGO HYE WAS FOUR TIMES AS OLD AS HER BROTHER. IN 1 YEAR SHE WILL BE TWICE AS OLD AS HE IS NOW. WHAT ARE THEIR AGES?
Found 2 solutions by sdmmadam@yahoo.com, beneke:
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
ELEVEN YEARS AGO HYE WAS FOUR TIMES AS OLD AS HER BROTHER. IN 1 YEAR SHE WILL BE TWICE AS OLD AS HE IS NOW. WHAT ARE THEIR AGES?
Let Hey's age be h years and her brother's age be b years.
11 yrs ago, Hye was 4 times as old as her brothher.
(h-11)=4(b-11) ----(1)
h-11 =4b-44
h=4b-44+11
h = 4b-33 ----(1)
In 1 year Hye will be twice as old his present age.
(h+1) = 2b ----(2)
Using (1) in (2), we get
[(4b-33)+1] = 2b
4b-33+1 = 2b
4b-32 = 2b
4b-2b = 32
2b = 32
b = 32/2 = 16
Putting h = 16 in (2),
h+1=2b
h+1 = 32
h = 32-1 = 31
Answer: Hye is 31 yrs old and her brother is 16 yrs old.
Verification: 11 years ago, Hye was(31-11) = 20 yrs old
and her brother was(16-11) = 5 yrs old
And 20 = 4 times 5. Thus the first information that 11years ago Hye was 4 times as old as his brother is right.
In 1 year Hye will be (31+1) = 32 years
And 32 = twice 16 = twice her brother's present age also correct.
Answer by beneke(1) (Show Source): You can put this solution on YOUR website!
11 yrs ago, Hye was 4 times as old as her brother.
(h-11)=4(b-11) ----(1)
h-11 =4b-44
h=4b-44+11
h = 4b-33 ----(1)
In 1 year Hye will be twice as old his present age.
(h+1) = 2(b +1) ----(2)
Using (1) in (2), we get
4b-33+1=2(b+1)
4b-32=2b+2
4b=2b+34
2b=34
b=17
So plug b=17 back into (1)
h = 4b-33
h=4(17)-33
h= 68-33
h=35
So, Hye is 35 and her brother is 17!

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