Question 632051: 5.You are 4 times as old as your sister. In 8 years time you will be twice as old as your sister. What are your ages now?
Please explains also why u do not add 8 to 4x during the equation and why does this have to have two equations
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let y = your age now
let x = your sister's age now.
since you are 4 times as old as your sister is now, you get:
y = 4x
in 8 years you will be 2 times as old as your sister is then.
in 8 years you will be y+8 years old
in 8 years your sister will be x+8 years old.
the equation that expresses the relationship between your age and your sister's 8 years from now is:
y+8 = 2(x+8)
you need to solve these 2 equations simultaneously to come up with a solution that is common to both equations.
your first equation is y = 4x
your second equation is y+8 = x+8
the first equation expresses the relationship between your age and your sister's age now.
the second equation expresses the relationship between your age 8 years from now and your sister's age 8 years from now.
from your first equation, you get y = 4x
you can susbtitute for y in the second equation to get:
y+8 = x+8 becomes:
4x+8 = 2(x+8)
notice that you DO add 8 to 4x.
simplify this equation to get:
4x+8 = 2x+16
subtract 2x from both sides of this equation and subtract 8 from both sides of this equation to get:
2x=8
divide both sides of this equation by 2 to get:
x=4
this represents your sister's age now.
y=4x represents your age now which is equal to 16.
you are 16 years old now and your sister is 4 years old now.
16 is equal to 4 times 4.
in 8 years you will be 16 + 8 = 24 years old.
in 8 years your sister will be 4 + 8 = 12 years old.
24 is equal to 2 times 12.
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you have 2 equations because you are expressing the relationship today (first equation) and the relationship 8 years from today (second equation).
you DO add 8 to 4x.
actually you are adding 8 to y, but since y = 4x, you are effectively adding 8 to 4x.
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the use of y is optional.
you could have said her age now is x and your age now is 4x and skipped the y.
in 8 years then your age would be 4x+8 and her age would be x+8 and the relationship would be 4x+8 = 2(x+8).
you get to the same place without using the y.
i find the use of the additional variable useful to clearly set in my mind what variable represents who's age, but it can be skipped if you know what you're doing up front and feel comfortable with not laying it all out systematically before solving.
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you can't get away from the fact that you have 2 equations to deal with.
the first equation expresses the relationship now.
the second equation expresses the relationship 8 years from now.
both equations have to be solved simultaneously to get a common solution for the variable of interest.
x was the variable that expressed the sister's age.
y or 4x was the variable that expressed the girl's age.
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