The difference of 2 positive numbers is 1/3 their sum. The sum of the squares of the 2 nums is 180.Find 2 nums

Answer 1

3(x-y) = x+y
3x-3y=x+y
2x = 4y
x = 2y

(2y)^2 + y^2 = 180

4y^2 + y^2 = 180
5y^2 = 180
y^2 = 36

y = 6
x = 2y = 12

Answer 2

Set up let statements. Let x = the first positive number. Let y be the second positive number.

Now set up equations.

The difference of 2 positive numbers is 1/3 their sum:

x - y = (1/3)(x + y)

The sum of the squares of the 2 nums is 180:

x^2 + y^2 = 180.

So we have 2 equations with 2 unknowns. The best way is to solve by substitution. But we first have to simplify the first expression and solve for one of the variables. Let's solve for x. You can also solve for y.

x - y = (1/3)(x + y)
First multiply both sides by 3 to get rid of all fractions.
3x - 3y = x + y

Next subtract items from both sides to get y's on one side and x's on the other.

2x = 4y ( subtract x from the right to the left, add 3y from the left to the right )

So now dividing by 2 on both sides we get x = 2y.

Now plug this result into the other equation to solve.

x^2 + y^2 = 180. But now x = 2y.
(2y)^2 + y^2 = 180
4(y^2) + y^2 = 180
5(y^2) = 180 (divide both sides by 5)
y^2 = 36
y = 6 or y = -6. However the question said "positive #'s"

So y = 6. Now using the fact that x = 2y, we can get x by plugging in 6 for y.

x = 2y
x = 2(6)
x = 12

So x = 12 and y = 6 . Your 2 numbers are 6 & 12

Answer 3

12 and 6

Answer 4

The two numbers you are looking for are 6 and 12.
12x12=144 + 6x6=36 = 180
12-6=6, which is 1/3rd the sum of 12+6=18.

Answer 5

Let x and y be the numbers. Then
x - y = 1/3(x +y)
and
x^2 + y^2 = 180

The first equation simplifies to
2x - 4y = 0
or x = 2y
Subtituting, we get
5y^2 = 180
y^2 = 36
y = 6
x = 12
The numbers are 12 and 6

Answer 6

x + y = z
x - y = z/3

2x = 4z/3
x = 2z/3

y = z/3

OK, so you have two numbers where one is double the other, like 4 and 2 or 8 and 4.

x^2 + y^2 = 180 . . . by x=2y
(2y)^2 + y^2 = 180
4y^2 + y^2 = 180
5y^2 = 180
y^2 = 36
y=6
x = 12

to check:

x^2 + y^2 = 180
12^2 + 6^2 = 180
144 + 36 = 180

Answer 7

x - y = 1/3(x + y)
x^2 + y^2 = 180

x - y = 1/3(x + y)
x - y = 1/3x + 1/3y
x = 1/3x + 4/3y
2/3x = 4/3y
x = (4/3 * 3/2)y
x = 2y

x^2 + y^2 = 180
(2y)^2 + y^2 = 180
4y^2 + y^2 = 180
5y^2 = 180
y^2 = 36
y = 6

x = 2y
x = 2(6)
x = 12

The two numbers are 12 and 6.

Answer 8

x - y = (1/3)(x + y)
x^2 + y^2 = 180

x - y = (1/3)(x + y)
3x - 3y = x + y
-4y = -2x
y = (1/2)x

x^2 + ((1/2)x)^2 = 180
x^2 + (1/4)x^2 = 180
(4/4)x^2 + (1/4)x^2 = 180
((4 + 1)/4)x^2 = 180
(5/4)x^2 = 180
5x^2 = 720
x^2 = 144
x = 12

y = (1/2)(12)
y = 6

The numbers are 12 and 6

Answer 9

12 - 6

Answer 10

A-B=1/3(A+B)
A2+B2=180

A=1/3(A+B)+B
A=1/3A+4/3B
2/3A=4/3B
A=2B

A2+B2=180
(2B)2 + B2=180
5B2=180
B2=36
B=6

AND SO, A=12