Question

The sum of two numbers is 180 and their
difference is 50. Find the numbers.

Answer 1

Answer:

Let x represent one of the numbers, and let y represent the other number.

Then we can write two equations:

x² + y² = 180

x² - y² = 108

By adding the two equations together, we get:

(x² + x²) + (y² - y²) = 180 + 108

2x² = 288

x² = 288 / 2

x² = 144

x = √144

x = ±12

To find the other number, substitute 12 in place of x in the first equation and solve for y:

(12)² + y² = 180

144 + y² = 180

y² = 180 - 144

y² = 36

y = √36

y = ±6

If only positive value solutions are desired, then the two numbers are 12 and 6.

If positive and negative values are acceptable, then the possible solutions are:

12, 6

-12, 6

12, -6

-12, -6