Homework Help

The square of Janets age is 400 more then the square of the sum of Kim's and Sue's...

user profile pic

primrose1e | eNotes Newbie

Posted October 21, 2013 at 7:39 PM via web

dislike 1 like

The square of Janets age is 400 more then the square of the sum of Kim's and Sue's ages. Kim's and Sue's ages total 10 less then Janets age. Find the square of the ages of Janet, Kim, and Sue

2 Answers | Add Yours

Top Answer

user profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted October 21, 2013 at 9:49 PM (Answer #1)

dislike 0 like

Let Janet's age be "x".

Kim+Sue's ages = x - 10

The square of Janet is `x^2.`

The square of the sum of Kim & Sue's ages = `(x-10)^2`

Since Janet's is 400 more,

`x^2 = (x-10)^2 + 400`

`x^2 = x^2-20x+100+400`

`20x = 500` 

`x = 25`

Janets is 25 years old, and Kim and Sue's ages together total 15.

The square of Kim's age is 625.  The square of the sum of Kim and Sues ages is 225.

1 Reply | Hide Replies

user profile pic

primrose1e | eNotes Newbie

Posted October 24, 2013 at 7:34 PM (Reply #1)

dislike 0 like

thank you so much

user profile pic

tonys538 | TA , Undergraduate | (Level 1) Valedictorian

Posted December 15, 2014 at 5:54 AM (Answer #2)

dislike 0 like

The square of Janet's age is 400 more then the square of the sum of Kim's and Sue's ages. Kim's and Sue's ages total 10 less then Janet's age.

If Janet, Kim and Sue's ages are represented by variables J, K and S we have:

J^2 = 400 + (K + S)^2

K + S = J - 10

Combining the two equations J^2 = 400 + (J - 10)^2

J^2 - (J - 10)^2 = 400

(J - J + 10)(J + J - 10) = 400

10*(2J - 10) = 400

2J - 10 = 40

2J = 50

J = 25

K + S = 15

This gives the square of Janet's age as 625 and the square of the sum of Kim and Sue's age as 225. It is not possible to determine the age of Kim and Sue individually.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes