Question

the sum of the 2 numbers is 180 and the difference of their squares is 108. Find the 2 numbers.

please show work.

Answer 1

x + y = 180

x = 180 - y

x^2 - y^2 = 108

(180 - y)^2 - y^2 = 108

32400 - 360y + y^2 - y^2 = 108

32400 - 360y = 108

32400 = 360y + 108

32292 = 360y

y = 32292/360

y = 897 / 10

x + y = 180

x + 897 / 10 = 1800 / 10

x = 1800 / 10 - 897 / 10

x = 903 / 10

Answer:  One of the numbers is 89.7 and the other number is 90.3

.

Check:  Is the difference of their squares 108?

.8154.09 - 8046.09

108 (good)

Answer 2

1...x+y=180, or y=180-x

2...x^2 -y^2=108

x^2 -(180-x)^2=108

x^2 -(x^2 -360x +180*180)=108

x^2-x^2 +360x -180*180=108

360x=108+32,400...=32,508

x=32,508/360=90.3

y=180-x=180-90.3=89.7

(x^2=8,154.09 & y^2=8,046.09)