Question 61612
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


 
  
 
 
 
 
 
#