SOLUTION: Sydney's present age is one-half of Marcus's present age. In 14 years, Sydney's age will be five-eighths of Marcus's age. Find their present ages.
Question 563451: Sydney's present age is one-half of Marcus's present age. In 14 years, Sydney's age will be five-eighths of Marcus's age. Find their present ages. Answer by Maths68(1474) (Show Source):
Sydney's present age is one-half of Marcus's
s=(1/2)m
s=m/2.....................(1)
In 14 years
Sydney will be = s+14
Marcus will be = m+14
Then
Sydney's age will be five-eigth of Marcus's
s+14=(5/8)(m+14)
8(s+14)=5(m+14)
8s+112=5m+70
8s=5m+70-112
8s=5m-42..................(2)
Put the value of s from (1) to (2)
8s=5m-42..................(2)
8(m/2)=m-42
4m=5m-42
4m-5m=-42
-m=-42
Multiply by -1 both sides of above equation
-m(-1)=-42(-1)
m=42
Put the value of m in (1)
s=m/2................(1)
s=42/2
s=21
Present age of Sydney = s = 21
Present age of Marcus = m = 42
Check
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In 14 years
Sydney will be = s+14 = 21+14 = 35
Marcus will be = m+14 = 42+14 = 56
Then
Sydney's age will be five-eigth of Marcus's
35=5/8(56)
35=(5)(56)/8
35=(5)(7)
35=35
