Question 28705: 1.Two years ago, Greg was 3 times as old as his brother. In four years, he will be only twice his brother's age. How old are they now?
2.Four years ago, Boyet was two years more than thrice as old as Bong. In another four years, Boyet will be two two years more than twice as old as Bong. How old is Boyet/
3.In five years, Yolly will be three years more than twice as old as her son. Five years ago, she was two years less than five times as old as her son. How old is Yolly?
4. The age of Diophantus, the father of algebra may be calculated from what is carved on his tombstone. It goes: "Diophantus youth lasted 1/6 of his life. He grew a beard after 1/12 more. After 1/7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly 1/2 as long as his father, and Diophantus died just after four years after his son. All of these add up to the years Diophantus lived." How old was Diophantus when he died?
5. When Ramon was 12 years old, his father was 40. How many years must pass for Ramon to be 8 years older than one-fourth as old as his father?
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! Here are all but the last two.
1.Two years ago, Greg was 3 times as old as his brother.
In four years, he will be only twice his brother's age.
How old are they now?
>>...Two years ago, Greg was 3 times as old as his brother...<<
Two years ago, Greg was G-2.
Two years ago, Brother was B-2
Two years ago, Greg was 3 times B-2 or 3(B-2)
Therefore G-2 = 3(B-2)
>>...In four years, he (Greg) will be only twice his brother's age.
In four years, Greg will be G+4
In four years, Brother will by B+4
In four years, Greg will be twice B+4, or 2(B+4)
Therefore G+4 = 2(B+4)
So you have the system of equations
G-2 = 3(B-2)
G+4 = 2(B+4)
CAn you solve that? If not post again.
Answer G=20, B=8
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2.Four years ago, Boyet was two years more than thrice as old as
Bong. In another four years, Boyet will be two two years more than
twice as old as Bong. How old is Boyet.
Their names both start with B, so change their names to X and Y
Four years ago, X was two years more than thrice as old as Y.
In another four years, X will be two two years more than twice
as old as Y. How old is X.
>>...Four years ago, X was two years more than thrice as old as Y...<<
Four years ago, X was X-4
Four years ago, Y was Y-4
Four years ago, X was two years more than thrice Y-4, or 3(Y-4)
Four years ago, X was two years more than 3(Y-4)
Four years ago, X was 3(Y-4) + 2
Therefore X-4 = 3(Y-4)+2
>>...In another four years, X will be two years more than twice as old as Y...<<
In another four years, X will be X+4
In another four years, Y will be Y+4
In another four years, X will be two years more than twice Y+4 or 2(Y+4)
In another four years, X will be two years more than 2(Y+4)
In another four years, X will be 2(Y+4) + 2
Therefore X+4 = 2(Y+4)+2
So you have the system
X-4 = 3(Y-4)+2
X+4 = 2(Y+4)+2
Solve it and you'll get X=30 and Y=12 or Boyet = 30 and Bong = 12
3.In five years, Yolly will be three years more than twice as old as
her son. Five years ago, she was two years less than five times as old
as her son. How old is Yolly?
>>...In five years, Yolly will be three years more than twice as old
as her son...<<
In five years, Yolly will be Y+5
In five years, Son will be S+5
In five years, Yolly will be three years more than twice S+5, or 2(S+5)
In five years, Yolly will be three years more than 2(S+5)
In five years, Yolly will be 2(S+5)+3
Therefore Y+5 = 2(S+5)+3
>>...Five years ago, she (Yolly) was two years less than five times
as old as her son...<<
Five years ago, she (Yolly) was Y-5
Five years ago, Son was S-5
Five years ago, she (Yolly) was 2 years less than 5 times S-5 or 5(S-5)
Five years ago, she (Yolly) was 2 years less than 5(S-5)
Five years ago, she (Yolly) was 5(S-5)-2
Therefore Y-5 = 5(S-5)-2
So you have this system of equations
Y+5 = 2(S+5)+3
Y-5 = 5(S-5)-2
Solve them and get Y=28, S=10
You do the other two, or post again
Edwin
AnlytcPhil@aol.com
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