Question

The sum of two numbers is 140, and their difference is 20. What are the two numbers?

Answer 1

60 and 80.

Explanation:

If the numbers are x and y:

x + y = 140

x - y = 20 Adding:

2x = 160

x = 80

So y = 140 - 80 = 60.

Answer 2

80 and 60

Explanation:

Expressing the Word Problem mathematically.

Let the first number be X.

Let the second number be Y.

From the question,

`x + y = 140 - - - - - (1) \\ x - y = 20 - - - - - (2) \\ From \: equation \: (2) \\ x = 20 + y - - - - - - (3) \\ Substitute \: equation \: 3 \: into \: 1 \\ 20 + y + y = 140 \\ 20 + 2y = 140 \\ 2y = 140 - 20 \\ 2y = 120 \\ Dividing \: bothsides \: by \: 2 \\ (2y)/(2) = (120)/(2) \\ y = 60 \\ Substitute \: y \: into \: quation \: 3 \\ x = 20 + 60 \\ x = 80 \\ Therefore, \: x = 80 \: and \: y = 60`

The two numbers are 80 and 60