Let's call these two numbers x and y. Our first goal is find a way to express one of the variables in terms of another.
x+y=27
x=27-y
Now that we have a value for x that can be expressed with y, let's plug it into the next problem.
x-y=5
(27-y)-y=5
27-2y=5
-2y=-22
y=11
Once we have a concrete value for y, we can use that to solve for x.
x=27-y
x=27-11
x=16
For a final step, use these numbers in the original problems to check the answer.
x+y=27 x-y=5
16+11=27 16-11=5
27=27 5=5
The numbers are 26 and 21
The numbers are 10 and 5
The numbers are 10 and 5
Let's name the first number x and the next number x + 1. So, x^2 - (x + 1)^2 = x^2 - (x^2 + 2x + 1) = x^2 - x^2 - 2x - 1 = - 2x - 1 = -(2x + 1) Thus we can say that, the difference between the squares of two consecutive numbers is equal to the opposite of their sum (means it is their sum, but as a negative number). Let's do some examples: 2, 3; 2 + 3 = 5 2^2 - 3^2 = 4 - 9 = -5 ( 5 and -5 are opposite numbers, and 5 is the sum of 2 and 3) 13, 14; 13 + 14 = 27 13^2 - 14^2 = 169 - 196 = -27 (27 and -27 are opposite numbers, and 27 is the sum of 13 and 14)
5 + (-3) = 2 5 - (-3) = 8 The two numbers are therefore 5 and -3.
4 + 5 = 9 4 and 5 are two numbers with the sum of 9 and have a difference of 5
They are 10 and 5
The two numbers are 10 and 5
5
8 and 5
10 and 5
5 & 21
the answer is 5
Three
The numbers are 26 and 21
17 and 5
2.25 and 2.75 :)