SOLUTION: Erum's age is 2/3 that of Zahra's .Two years ago Erum's age was 1/2 of what Zahra's age will be in 5 year's time. How old is Zahra now ?

Algebra ->  Expressions-with-variables -> SOLUTION: Erum's age is 2/3 that of Zahra's .Two years ago Erum's age was 1/2 of what Zahra's age will be in 5 year's time. How old is Zahra now ?      Log On


   

Question 189338: Erum's age is 2/3 that of Zahra's .Two years ago Erum's age was 1/2 of what Zahra's age will be in 5 year's time. How old is Zahra now ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Let E = Erum's present age
Lot Z = Zahra's present age
:
Write an equation for each statement:
;
Erum's age is 2/3 that of Zahra's .
E = 2%2F3Z
:
Two years ago Erum's age was 1/2 of what Zahra's age will be in 5 year's time.
(E-2) = 1%2F2(Z+5)
:
Multiply both sides by 2:
2(E-2) = Z + 5
:
2E - 4 = Z + 5
:
2E = Z + 5 + 4
:
2E = Z + 9
:
How old is Zahra now ?
:
Substitute 2%2F3Z for E in the above equation
2(2%2F3Z) = Z + 9
4%2F3Z = Z + 9
Subtract Z from both sides
4%2F3Z - 3%2F3Z = 9
1%2F3Z = 9
Multiply both sides by 3
Z = 27 yrs is Zahra's age now
:
The 2%2F3(27) = 18 yrs is Erum's age now
:
:
Check solution in the statement:
"Two years ago Erum's age was 1/2 of what Zahra's age will be in 5 year's time."
(18-2) = .5(27 + 5)