Question

find two mixed numbers so that the sum is 8 4/8 and the difference is 2 2/8

Answer 1

Using a system of equations, it is found that the numbers with the desired sum and difference are given by:

$x = 3\frac{4}{8}, y = 1\frac{1}{8}$

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are x and y. Initially applying the conversion from mixed to fraction, the system is:

$x + y = \frac{36}{8} \rightarrow y = \frac{36}{8} - x$

$x - y = \frac{18}{8}$

Since $y = \frac{36}{8} - x$:

$x = \frac{18}{8} + y$

$x = \frac{18}{8} + \frac{36}{8} - x$

$2x = \frac{54}{8}$

$x = \frac{54}{16}$

$x = \frac{27}{8}$

Then y is given by:

$y = \frac{36}{8} - x = \frac{36}{8} - \frac{27}{8} = \frac{9}{8}$

Now we apply the conversion to mixed numbers, as 27 divided by 8 has quotient 3 and remainder 4, and 9 divided by 8 has quotient and remainder 1, hence:

$x = 3\frac{4}{8}, y = 1\frac{1}{8}$

More can be learned about a system of equations at https://brainly.com/question/24342899