SOLUTION: Thank you very much for taking the time to help me! My question relates to fractional algebra. Question: Sydney�s present age is one-half of Marcus�s present age. In 12

Question 934476: Thank you very much for taking the time to help me!
My question relates to fractional algebra.

Question:
Sydney�s present age is one-half of Marcus�s present age. In 12 years, Sydney�s age will be five-eighths of Marcus�s age. Find their present ages

My Attempt:
Let:
s = Sydney's age
m = Marcus's age
Therefore:
Sydney's current age = 1/2m
In 12 years time:
s = 5/8(m + 12)
m = m + 12

The equation I set up is:
5/8(m+12) = m + 12

8 [5/8(m + 12)] = 8 (m + 12)
5(m + 12) = 8m + 96
5m + 60 = 8m + 96
5m - 8m + 60 = 8m - 8m +96
-3m + 60 = 96
-3m + 60 - 60 = 96 - 60
-3m = 36

-3m/3 = 36/3
-m = 12
m = -12
Obviously this is the wrong answer as an age cannot be negative. Also, the textbook provided me with the answer of 18 for Sydney and 36 for Marcus.
Thank you very much for all your help.
Kind regards,
Mark Beaton

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let m be Marcus's age, s be Sydney's age then we have
s = m/2
s+12 = 5/8*(m +12)
substitute for s in second equation
m/2 +12 = 5/8*(m +12)
m/2 + 12 = 5m/8 + 5/8*12
multiply both sides of = by 8
4m +96 = 5m + 60
m = 36
s = 18

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