# Rode is 10 years older than macoy. Marten is 6 years younger than rode. If the sum of their ages is 65, how old is each?

1
by dionisiovellega

2014-11-14T21:59:54+08:00
Let 'x' be Rode's age
'y' be Macoy's age
'z' be Marten's age
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From the statement, 'Rode is 10 years older than Macoy'
x = y + 10    ----equation 1
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From the statement, 'Marten is 6 years younger than Rode'
z = x - 6    ------equation 2
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The sum of their ages is 65
x + y + z = 65    -----equation 3
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From equation 1
x = y + 10
Expressing y in terms of x you'll have
y = x - 10    ----equation 1'
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Substitute equations 1' and 2 to equation 3
x + y + z = 65
x + (x-10) + (x-6) = 65
x + x - 10 + x - 6 = 65
x + x + x = 65 + 10 + 6
3x = 81
x = 27 ---Rode's age
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Substitute x=27 to equations 1' and 2
y = x - 10
y = 27 - 10
y = 17  ---Macoy's age
z = x- 6
z = 27 - 6
z = 21  ----Marten's age
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Therefore Rode is 27 yrs old, Macoy is 17 yrs old and Marten is 21 yrs old.