One number is 10 more than twice another. Their sum is 1. Find the numbers.

One number is 10 more than twice another. Their sum is 1. The numbers are - 3 and 4

Solution:

Given that one number is 10 more than twice the other.

Let us consider the two numbers as "x" and "y"

First number = x

Second number = y

From question, consider "y" is 10 more than twice the "x". This can be represented

y = 10 + 2x - eqn 1

given that the sum of numbers is 1. Hence we get

x + y = 1

substituting the value of "y" we get

x + 10 + 2x = 1

3x + 10 = 1

3x = - 9

x = - 3

substitute x = - 3 in eqn 1 to get the value of "y"

y = 10 + 2 (-3)

y=10 - 6 = 4

hence the two numbers are - 3 and 4