Mrs landau has two daughters, serval and lynx. The highest common factor and the lowest common multiple of their age are 3 and 168 respectively. If serval is 3 years older than her sister, find serval’s age
Q. Mrs landau has two daughters, serval and lynx. The highest common factor and the lowest common multiple of their age are 3 and 168 respectively. If serval is 3 years older than her sister, find serval’s age
Denote Ages: Let's denote Serval's age as S and Lynx's age as L. We know that S=L+3.
HCF and LCM: The highest common factor (HCF) of their ages is 3. This means that both S and L are multiples of 3.
Equation Setup: The lowest common multiple (LCM) of their ages is 168. Since LCM of two numbers a and b is given by (a×b)/HCF(a,b), we can write the equation S×L=168×3.
Substitution: Substitute S=L+3 into the equation: (L+3)⋅L=504.
Expand Equation: Expand the equation: L2+3L=504.
Rearrange Quadratic: Rearrange the equation to form a quadratic equation: L2+3L−504=0.
Factor Quadratic: Factor the quadratic equation: (L+21)(L−24)=0.
Solve for L: Solve for L: L=−21 or L=24. Since age cannot be negative, L=24.
Find Serval's Age: Now, find Serval's age using S=L+3: S=24+3.