Three friends, Hannah, Jeremy and Delmon, were watching the Tigers game on TV. The Tigers were losing, so they started talking about how old each of them was. Jeremy, who was the oldest, noticed that they were all between the ages of 11 and 30. Hannah noticed that the sum of their ages was 70. Delmon, the youngest, burst out, "The difference between me and the oldest is more than 10 years!" Hannah then realized that the difference between her age and each of the guys was more than 5 years. How old was each person?

The age of  Hannah, Jeremy and Delmon are 20 years , 25 years and 25 years respectively

Step-by-step explanation:

Let H , J and D be the age of  Hannah, Jeremy and Delmon respectively.

We are given that Hannah noticed that the sum of their ages was 70.

H+J+D=70---1

Now we are given that Delmon, the youngest, burst out, "The difference between me and the oldest is more than 10 years!"

J-D>10

Now we are given that Hannah then realized that the difference between her age and each of the guys was more than 5 years.

So, D-H>5

J-H>5

D-H=5---2

J-H=5

So, D=J

Substitute in 1

2D+H=70 --3

Substitute the value of H from --3 in 2

D-70+2D=5

D=25

So, J = 25

Substitute values in 1

H+25+25=70

H=20

Hence the age of  Hannah, Jeremy and Delmon are 20 years , 25 years and 25 years respectively

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8