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55. If the sum of two numbers is 20 and their difference is 4, find the numbers.

A. 12 and 8
B. 14 and 6
C. 15 and 5
D. 13 and 7


Sagot :

Certainly! Let's solve the problem step-by-step.

We are given two key pieces of information about two numbers:
1. Their sum is 20.
2. Their difference is 4.

Let's denote these two numbers as [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

From the given information, we can set up the following system of equations:
1. [tex]\( x + y = 20 \)[/tex]
2. [tex]\( x - y = 4 \)[/tex]

To find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we can solve these equations simultaneously.

Step 1: Add the two equations

[tex]\[ (x + y) + (x - y) = 20 + 4 \][/tex]

This simplifies to:

[tex]\[ x + y + x - y = 24 \][/tex]

[tex]\[ 2x = 24 \][/tex]

Step 2: Solve for [tex]\( x \)[/tex]

[tex]\[ x = \frac{24}{2} \][/tex]

[tex]\[ x = 12 \][/tex]

Step 3: Substitute the value of [tex]\( x \)[/tex] back into the first equation

[tex]\[ 12 + y = 20 \][/tex]

Step 4: Solve for [tex]\( y \)[/tex]

[tex]\[ y = 20 - 12 \][/tex]

[tex]\[ y = 8 \][/tex]

So, the two numbers are [tex]\( x = 12 \)[/tex] and [tex]\( y = 8 \)[/tex].

Therefore, the correct answer is:

(a) 12 and 8
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