Question

Mrs John is 5 times older than her son .3 years ago the product of their ages was 185 how old is Mrs John

Answer 1

Mrs J - > X years ago,

Her son - > Y years old 

$X =5*Y\\$

$\begin{alignedat}{2} (5&Y-3)&(Y-3) = 185 \end{alignedat}$

$5*Y^{2}-18*Y-176=0\\$

a=5, b=-18, c=-176=0

$D=b^{2}-4*a*c,$

$D=(-18)^{2}-4*1*(-176)=62^2,$

$Y1=(-b+\sqrt{D})/(2*a),\\ Y1=(-(-18)+\sqrt{62^2})/(2*5)=8,\\ Y2=(-b-\sqrt{D})/(2*a), \\ Y2=(-(-18)-\sqrt{62^2})/(2*5)=-4.4. \\$

The age must be greater than 0, so Y=8,

X=5*Y=5*8=40.

Mrs John is 40 years old, her son is 8 years old,

Checking: (40-3)*(8-3)=185.

Answer: Now Mrs John is 40 years old, her son is 8 years old.