Question 208027: in 3 years,alex will be 3 times as old as his sister precy,a year ago alex was 7 times as old as precy.how old are they now
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in 3 years, alex will be 3 times as old as his sister precy, a year ago alex was 7 times as old as precy. how old are they now
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alex is x years old now
precy is y years old now
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in 3 years, alex will be 3 times as old as his sister precy
3 years from now, alex will be (x + 3) years old.
3 years from now, precy will be (y + 3) years old.
3 years from now, alex will be 3 times as old as his sister precy.
equation for this would be:
(x + 3) = 3 * (y + 3)
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a year ago alex was 7 times as old as precy.
a year ago, alex was (x-1) years old.
precy was (y-1) years old.
a year ago, alex was 7 times as old as precy.
equation for this would be:
(x - 1) = 7 * (y - 1)
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you have 2 equations that express the relationship between alex's age and precy's age.
those 2 equations are:
(x + 3) = 3 * (y + 3)
and
(x - 1) = 7 * (y - 1)
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you need to solve both equations simultaneously to get the same solution that satisfies both equations at the same time.
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simplifying these equations and converting them to standard form, they become:
x - 3y = 6
and
x - 7y = -6
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if we subtract the second equation from the first, then the x will cancel out and we'll get:
4y = 12
divided both sides of the equation by 4 gets:
y = 3
if y = 3, we can then solve for x in either equation:
from the first equation, we get:
x - 9 = 6 resulting in x = 15
from the second equation, we get:
x - 7y = -6 which becomes x - 21 = -6
this results in x = 15
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alex is 15 years old now.
precy is 3 years old now.
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1 year ago alex was 14 years old and precy was 2 years old.
14 / 2 = 7 satisfying the part of the equation for one year ago.
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3 years from now alex will be 18 years old and precy will be 6 years old.
18 / 6 = 3 satisfying the part of the equation for 3 years from now.
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answer to the question is alex is 15 years old and precy is 3.
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