Question

john is five years older than his sister. the product of their present ages is 150.John's present age is (blank) years, and this sister's present age is (blank) yearsso i believe you have to answer this with the quadratic formula but I'm not sure. please help

Answer 1

Given

John is five years older than his sister.

Product of their present ages is 150

Find

Present age of John and his sister

Step-by-step explanation

Let his sister's age be x

so, according to the question ,

John's age = 5 + x

product of their present age will be given as 150

so ,

`\begin{gathered} x(x+5)=150 \\ x^2+5x=150 \\ x^2+5x-150=0 \\ x^2+15x-10x-150=0 \\ x(x+15)-10(x+15)=0 \\ (x+15)(x-10)=0 \\ x=-15,10 \end{gathered}`

age never be negative , so neglect negative value .

hence , age of his sister = 10

and john's age = x + 5 = 15

Final Answer

Hence , John's present age is 15 years, and his sister's present age is 10 years.