SOLUTION: Janet is three years older than her sister Julie. Janet's brother is eight years younger than their sisterjulie. The sum of all their ages is 55. How old are Janet, julie and their

Question 925933: Janet is three years older than her sister Julie. Janet's brother is eight years younger than their sisterjulie. The sum of all their ages is 55. How old are Janet, julie and their brother?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = janet age now
y = julie age now
z = brother age now
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x + y + z = 55
x = y + 3
z = y - 8
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put the system of linear equations into standard form
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x + y + z = 55
x - y = 3
y - z = 8
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution by matrix method:
x = janet age now = 23
y = julie age now = 20
z = brother age now = 12
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by elimination:
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x + y + z = 55
(x - y = 3)(-1)
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x + y + z = 55
-x + y = -3
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add the above two equations:
2y + z = 52
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2y + z = 52
y - z = 8
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add the above two equations:
3y = 60
y = 20
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-x + y = -3
-x + 20 = -3
-x = -23
x = 23
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y - z = 8
20 - z = 8
-z = -12
z = 12
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solution by elimination matches solution by matrix method:
x = janet age now = 23
y = julie age now = 20
z = brother age now = 12
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