Answer:

7.65 is the age of the youngest son.

Step-by-step explanation:

Let :

x - the age of the younger son

2x+3 - the age of the older son

x(2x+3) = 140

2x² +3x -140 = 0

using quadratic formula:

x = 7.65

x = -9.15

since we are solving for the age we take the positve value of x = 7.65

So : 7.65 is the age of the youngest son:

Checking:

solve for the older son:

2x+3

2(7.65)+3

= 18.3

x(3+2x) = 140

7.65(18.3) = 140

139.99 = 149

140 = 140