Question

Find the value of two numbers if their sum is 12 and their difference is 4

a
x=4 y=8

b
x=8 y= 4

c
x=6 y=12

Answer 1

Let's denote the two numbers as \(x\) and \(y\). According to the problem, we have the following two equations based on the given conditions:

1. \(x + y = 12\) (their sum)
2. \(x - y = 4\) (their difference)

We can solve these equations simultaneously.

First, we can solve for \(x\) and \(y\) using the two equations:

From equation 1:
\[ y = 12 - x \]

Now we can substitute \(y\) in equation 2:
\[ x - (12 - x) = 4 \]
\[ x - 12 + x = 4 \]
\[ 2x - 12 = 4 \]
\[ 2x = 16 \]
\[ x = 8 \]

Now substitute \(x\) back into the equation for \(y\):
\[ y = 12 - 8 = 4 \]

So the numbers are \(x = 8\) and \(y = 4\).

Looking at the options provided:
- a: \(x = 4, y = 8\)
- b: \(x = 8, y = 4\)
- c: \(x = 6, y = 12\)

The correct answer is:
**b: \(x = 8, y = 4\)**.