SOLUTION: You are 4 years older than your brother. Two years ago you were 1.5 x older than him. How old are you know?

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Question 171037: You are 4 years older than your brother. Two years ago you were 1.5 x older than him. How old are you know?
Found 2 solutions by solver91311, gonzo:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I think you meant to say "How old are you now?"

You are x years old now.

Your brother is then x - 4 years old now.

Two years ago, you were x - 2 years old, and your brother was x - 4 - 2 or x - 6 years old.

Your age two years ago (x - 2) is 1.5 times your brothers age two years ago, or 1.5(x - 6). So you can write:

x-2+=+1.5%28x-6%29

Solve the equation for x to get your age now. Once you have solved the equation, check your work: Subtract 4 from your answer to get your brother's age now. Then subtract 2 from each of yours and your brother's ages to get the ages two years ago. Verify that your age 2 years ago is one and one-half times your brother's age 2 years ago.


Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
let your age be x.
let your brother's age be y.
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you are now 4 years older than your brother:
x = y + 4
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two years ago you were 1.5 times older than your brother:
x - 2 = 1.5 * y
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how old are you now?
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you have 2 equations that need to be solved simultaneously (the same values for x and y make both equations true).
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one way to solve this is as follows:
leave your first equation as it is:
x = y + 4
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take your second equation and add 2 to both sides:
x = 1.5*y + 2
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since both equations equal to x, then both equation equal to each other:
y + 4 = 1.5*y + 2
solve for y:
subtract 2 from both sides of the equation:
y + 4 - 2 = 1.5*y + 2 - 2
simplify:
y + 2 = 1.5 * y
subtract y from both sides of the equation:
y - y + 2 = 1.5 * y - y
simplify:
2 = .5 * y
multiply both sides of equation by 2:
2 * 2 = 2 * .5 * y
simplify:
4 = y
exchange sides of equation (value remains the same):
y = 4
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you now have y = 4.
take either equation and solve for x:
take:
x = y + 4
substitute 4 for y:
x = 4 + 4 = 8
you now have:
x = 8
y = 4
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the first equation is satisfied since you used it to find x.
take the second equation and substitute 4 for y and 8 for x:
x - 2 = 1.5 * y
substitute for x and y:
8 - 2 = 1.5 * 4
simplify:
6 = 1.5 * 4
6 = 6
equation is true.
you are 8 years old now (x = 8).
your brother is 4 years old now (y = 4).
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