The sum of two numbers is 172. Their difference is 10. What are the numbers?

The numbers are 91 and 81

Step-by-step explanation:

Let:

x be the first number.

y be the second number.

The sum of two numbers is 172.

x + y = 172

Their difference is 10.

x - y = 10

Try to arrange for solving x:

x - y = 10

x = 10 + y

Now substitute the x to the first equation.

x + y = 172

(10 + y) + y = 172

10 + y + y = 172

10 + 2y = 172

2y = 172 - 10

2y = 162

y = 162 : 2

y = 81

Now solve for x:

x + y = 172

x + (81) = 172

x = 172 - 81

x = 91

Now let's check one more time:

The sum of two numbers is 172:

91 + 81 = 172

172 = 172 (correct)

Their difference is 10:

91 - 81 = 10

10 = 10 (correct)

Step-by-step explanation:

let x, y two numbers : x+y = 172 ... (1)

x - y = 10 ... (2)

add (1) and (2) : 2x = 182

so : x = 182/2 = 91

put x = 91 in (1) : 91+y = 172

y = 172 - 91 = 81