SOLUTION: i need help with this problems. 1. rose is 6 years older than her sister cora. in four years, she will be nine years more than one-half as old as cora. how old are the girls now

Question 28702: i need help with this problems.
1. rose is 6 years older than her sister cora. in four years, she will be nine years more than one-half as old as cora. how old are the girls now?
2. rolly is 9 years younger than greg. in seven years, he will be two years more than one-half as old as greg. find their present ages.
3. a mother is 20 years older than her daughter. five years from now, she will be thrice as old as her daughter will then be. how old is the daughter?
4. a mother is twice as old as her daughter. eight years from now, she will be twenty years older than her daughter will then be. how old is the mother now?
5. edwin is twice as old as ruel. in three years, edwin will be 13 years less than twice as old as jill. find their present ages.
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
1. rose is 6 years older than her sister cora. In four years, she will be nine years
more than one-half as old as cora. how old are the girls now?
Let Rose be a years old and let Cora be b years old.
Rose is 6 years older than her sister cora.
a is 6 more than b which means
a= b+6 ----(1)
In four years, she will be nine years more than one-half as old as cora.
Rosa is now a yrs old and in 4 yrs she will be (a+4) yrs old
Cora is now b yrs old. and in 4 yrs she will be (b+4) yrs old
(a+4) will be 9 yrs more than (1/2)(b+4)
(a+4) - (1/2)(b+4) = 9
multiplying by 2 through out.
2(a+4)-(b+4)=(2X9)
2a+8-b-4=18
2a-b+8-4=18
2a-b=18-4
2a-b=14 ----(2)
using a= b+6 ----(1) in this
2(b+6)-b = 14
2b+12-b=14
12+2b-b =14
12+b =14 gives b= 14-12 = 2
b= 2 in (1) we get a= b+6 = 2+6 =8
a=8, b=2
Answer: Rosa is 8 yrs old and Cora is 2 yrs old.
Verification: Rosa is 8 yrs old and is of course 6 more than 2 which is Cora’s age.
In 4 years Rosa wii be (8+4) yrs old and Cora will be (2 +4)yrs old.
And of course 12 is 9 more than half of 6
2.) Rolly is 9 years younger than greg.
In seven years, he will be two years more than one-half as old as greg. find their present ages.
Let Rolly be a years old and let Greg be b years old.
Rolly is 9 years younger than Greg
a is 9 less than b
a = b-9 ----(1)
in seven years.he will be two years more than one-half as old as greg.
In 7 yrs Rolly will be (a+7) and Greg will be (b+7)
(a+7) is 2 more than (1/2)(b+7)
(a+7) = (1/2)(b+7) +2
Multiplying by 2 through out
2(a+7)=(b+7)+(2X2)
2a+14=b+7+4
2a+14=b+11
2a-b = 11-14
2a-b=-3 ----(2)
Using (1) in (2)
2(b-9)-b=-3
2b-18-b=-3
(2b-b)=-3+18
b=15
Putting b=15 in (1) a= b-9 = 15-9 = 6
Answer:Rolly is 6 yrs old and Greg is 15 years old
Verification: 6 is 9 less than 15 which answers Rolly is 9yrs younger than Creg
In 7 yrs Rolly’s age will be (6+7) = 13 years and Greg’s age will be (15+7) = 22 years and then Rolly should be 2 more than half of Greg and of course13 is 2 more than (1/2) of (22)
3)A mother is 20 years older than her daughter. five years from now, she will be thrice as old as her daughter will then be. how old is the daughter?
Let the mother be M yrs old and let the daughter be D yrs old.
M is 20 more than D That is M= D+20 ----(1)
Five years from now, mother will be (M+5 ) and daughter will be (D+5) yrs old.
Then mother will be thrice as old as the daughter
(M+5) = 3(D+5) ----(2)
Putting (1) in (2)
[(D+20)+5] = 3D+15
D+25 = 3D+15
25-15=3D-D
10=2D
D=10/2 = 5
Putting D=5 in (1)
M=D+20----(1)
M=5+20=25
Answer: Mother is 25 yrs old and daughter is 5 yrs old.
Verification: Mother is 25 and is 20 more than 5 which is the daughter’s age.
After 5 years, mother will be 30 and daughter will be 10yrs and 30 is of course thrice 10
4. A mother is twice as old as her daughter. eight years from now, she will be twenty years older than her daughter will then be. how old is the mother now?
Let the mother be M yrs old and let the daughter be D yrs old.
M is twice D That is M= 2D ----(1)
Eight years from now, mother will be (M+8 ) and daughter will be (D+8) yrs old.
Then mother will be 20 more than the daughter
(M+8) = (D+8) +20 ----(2)
Putting (1) in (2)
(2D+8) = (D+8) +20
2D-D = 20
D=20
Putting D=20 in (1)
M=2D----(1)
M=2X20=40
Answer: Mother is 40 yrs old and daughter is 20 yrs old.
Verification: Mother is 40 and is twice 20 which is the daughter’s age.
After 8 years, mother will be 48 and daughter will be 28 yrs and 48 is of course 20 more than 28

The problem is wrong. Here is the corrected one.
5. Edwin is thrice as old as Ruel. In three years, Edwin will be 13 years more than twice as old as Ruel. find their present ages.
The problem is wrong. Here is the corrected one.
Let Edwin be E years old and let Ruel be R years old.
Edwin is thrice as old as Ruel
E=3R----(1)
In three years, Edwin will be 13 years more than twice as old as Ruel.
In 3 yrs Edwin will be (E+3) and Ruel will be (R+3)
(E+3) is 13 yrs more than twice (R+3)
(E+3) =2(R+3)+13 ----(2)
Putting (1) in (2)
(3R+3)=2R+6+13
3R-2R=19-3
R=16
Putting R=16 in (1) gives E = 3R = 3X16 = 48
Answer: Edwin is 48 years old and Ruel is 16 yrs old
Verification: Edwin is 48 yrs old which is thrice 16= Ruel’s age.
In 3 yrs Edwin’s age will be (4 8 +3) = 51 years and Ruel’s age will be (16+3) = 19 years and then Edwin should be 13 more than twice Ruel and of course 51 is 13 more than twice(19)

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