Question about Vivendi Math Blaster Algebra (03763) for PC, Mac

# Four years ago allan was three less than twice roys age in 5years allan will be 6yeras older than roy how old are they?

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Allan is 19 and Roy is 13.

Solution:

First we have 2 variables, their ages: I used Allan = x & Roy = y
Equation 1: X - 4 = 2*(Y-4) - 3
We can ignore the 5 years in the second part of the statement. Allan will always be 6 years older than Roy whether it be 5 years from now or ten years form now.
Equation 2: X = Y + 6

Substitute Y + 6 for X in equation 1:
X - 4 = 2*(Y-4) - 3 becomes Y + 6 - 4 = 2*(Y-4) - 3
That simplifies to Y + 2 = 2Y - 8 - 3
Rewrite it again: Y + 2 = 2Y - 11
Add 11 to both sides: Y + 13 = 2Y
Subtract Y from both sides: 13 = Y

Now plug 13 in for y in Equation 2
X = Y + 6
X = 13 + 6
X = 19

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### Cory is 6 years older than her sister.Four years ago, she was 4 times as old her sister.how old is cory now?

let c = cory's age now let s = her sisters age now
cory's age now = sisters age + 6 years
=> c = s + 6
4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)
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We can then use simultaneous equations to solve the two equations
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We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12
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### Alvin is now 20 years older than his son.In 10 years,he will be twice as old as his son's age.What are their present age's?

Christine,

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