SOLUTION: lucy is 4 timew as old as Amy. Three years ago,Lucy was 13 times as old as Amy. How old is Lucy now? #2 In 18 years, Jenny will be three times as old as she is now. How old is

Question 61612: lucy is 4 timew as old as Amy. Three years ago,Lucy was 13 times as old as Amy. How old is Lucy now?
#2 In 18 years, Jenny will be three times as old as she is now. How old is she?
#3 An antique desk is 25 years older than an antique chair. In 15 years, the desk will be 2 times as old as the chair. Find the present age of the furniture.
#4 Steve is twice as old as Sylvia, Sylvia is three years older than Jacob. 4 years ago, Sylvia was twice Jacobs age. How old is Sylvia?
#5 Greg is three times as old as Meg. Ten years from now, Greg's age will be one year more than twice Meg's age at that time. How old are Greg and Meg now?
#6 twenty five years ago, haily was five more than one third as old as jason was. Today, Jason is twenty six less than two times the age of haily. How old is jason now?

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Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Lucy is 4 times as old as Amy.
L = 4*A
Three years ago,Lucy was 13 times as old as Amy.
L - 3 = 13(A-3)
Using the 1st equation, substitute 4A for L, Solve for A:
4A - 3 = 13(A-3)
4A - 3 = 13A - 39
4A - 13A = - 39 + 3
-9A = -36
A = -36/-9
A = 4 yrs old now,:
:
How old is Lucy now?
L = 4A, therefore L = 16 yrs old now
:
:
#2 In 18 years, Jenny will be three times as old as she is now.
3J = J+18
3J - J = 18
2J = 18
J = 9 years old:
Check: 9 + 18 = 3(9)
:
:
#3 An antique desk is 25 years older than an antique chair.
D = C + 25
In 15 years, the desk will be 2 times as old as the chair.
D + 15 = 2(C + 15)
D + 15 = 2C + 30
D = 2C + 30 - 15
D = 2C + 15
Find the present age of the furniture.
Substitute (C+25) for D in the above equation
C + 25 = 2C + 15
25 - 15 = 2C - C
C =10, then desk is obviously 35 yrs old
:
:
#4 Steve is twice as old as Sylvia,
St = 2*Sy
Sylvia is three years older than Jacob.
Sy = (J+3)
4 years ago, Sylvia was twice Jacobs age.(Sy -4) = 2(J-4)
Sy - 4 = 2J - 8
Sy = 2J - 8 + 4
Sy = 2J - 4
Substitute (J+3) for Sy
J + 3 = 2J - 4
3 + 4 = 2J - J
J = 7 yrs old
How old is Sylvia?, We know she is 3 yrs older than Jacob: 7 + 3 =10 yrs old
What did Steve have to do with this problem??
:
:
#5 Greg is three times as old as Meg.
G = 3M
Ten years from now, Greg's age will be one year more than twice Meg's age at that time.
G + 10 = 2(M+10) + 1
G = 2M + 20 + 1 - 10
G = 2M + 11
How old are Greg and Meg now?
Substitute 3M for G:
3M = 2M + 11
3M - 2M = 11
M = 11 is Meg's age, Greg must be 3(11) = 33 yr old
:
:
#6 twenty five years ago, haily was five more than one third as old as jason was.
H - 25 = (J-25)/3 + 5
H = (J-25)/3 + 5 + 25
H = (J-25)/3 + 30
#Today, Jason is twenty six less than two times the age of haily. How old is Jason now?
J = 2H - 26
Substitute [((J-25)/3)+30] for H in the above equation:
J = 2[((J-25)/3) + 30] - 26
J = 2J-50/3 + 60 - 26
J = (2J-50)/3 + 34
J - (2J-50)/3 = 34
Mult eq by 3:
3J - (2J - 50) = 102
3J - 2J + 50 = 102
J = 102 - 50
J = 52 yrs old is Jason's age
Find Haily's age:
H = (J-25)/3 + 30
H = (52-25)/3 + 30
H = 27/3 + 30
H = 39 yrs is Haily's age

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