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The sum of two numbers is 49, and the difference between the numbers is 5. Find the numbers.

The numbers are _______.
(Use a comma to separate answers as needed.)

Sagot :

GinnyAnswer
Let's solve the problem step by step.

We're given two pieces of information about two numbers, which we'll call \( x \) and \( y \):

1. \( x + y = 49 \)
2. \( x - y = 5 \)

To find the values of \( x \) and \( y \), we can use the method of solving simultaneous equations.

First, let's add the two equations:

[tex]\[ (x + y) + (x - y) = 49 + 5 \][/tex]

This simplifies to:

[tex]\[ 2x = 54 \][/tex]

Now, solve for \( x \):

[tex]\[ x = \frac{54}{2} = 27 \][/tex]

Next, substitute \( x = 27 \) back into the first equation to find \( y \):

[tex]\[ 27 + y = 49 \][/tex]

Now, solve for \( y \):

[tex]\[ y = 49 - 27 = 22 \][/tex]

So, the two numbers are:

[tex]\[ (27, 22) \][/tex]

Therefore, the numbers are 27 and 22.
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