Question

The sum of two numbers is at least 8, and the sum of one of the numbers and 3 times the second mumber isno more than 15.

Answer 1

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: