1 Answer

Wootsbot · Answer 1 · 2023-10-30T12:51:51+0000

As given by the question

There are given that the sum of the two numbers is at least 8.

Now,

Let the unknown numbers be x and y

Then,

If the sum of the two numbers is at least 8 then:

$x+y\ge8$

Similarly, the sum of one of the numbers and 3 times the second number is no more than 15

Then,

$x+3y\leq15$

Now,

From the both of the inequality:

$\begin{gathered} x+y\ge8 \\ x+3y\leq15 \end{gathered}$

Then, find the first and second nuber:

So,

$\begin{gathered} x+y\ge8 \\ x\ge8-y\ldots(a) \end{gathered}$

Then, Put the value of x into the second equation

Then,

$\begin{gathered} x+3y\leq15 \\ 8-y+3y\leq15 \\ 8+2y\leq15 \\ 2y\leq15-8 \\ y\leq(7)/(2) \\ y\leq3.5 \end{gathered}$

Then,

Put the value of y into the equation (a)

$\begin{gathered} x\ge8-y \\ x\ge8-3.5 \\ x\ge4.5 \end{gathered}$

Hence, the first number and second number is shown in below:

$\begin{gathered} x\ge4.5 \\ y\leq3.5 \end{gathered}$

The graph of the given result is shown below:

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