Question

Need help with this and this is all one problem

Answer 1

Check the answers below, please.

1) In this question we need to interpret that text, and then translate it into a mathematical expression. Precisely, a system of linear inequalities.

a) Gathering the data from the text, we can write out the following system:

`\mleft\{\begin{matrix}r+w\geq4 \\ 220r+110w\geq600\end{matrix}\mright.`

b) Now, we need to plot that graph to find the region of possible solutions. The darkest region will be the one that contains the solution.

This is equivalent to the last graph.

c) To answer this question, we'll need to plug into both of those equations w=3 and r=1 and verify if that remains true.

`\begin{gathered} \begin{matrix}r+w\geq4\end{matrix} \\ 1+3\ge4 \\ 4\ge4\: True! \\ \: -- \\ 220r+110w\geq600 \\ 220(1)+110(3)\ge600 \\ 220+330\ge600 \\ 550\ge600\: False! \end{gathered}`

So, the answer is No.

d) Similarly, let's do the same for walking 2 miles and running two miles:

`\begin{gathered} 2+2\ge4 \\ 4\ge4\: True! \\ 220(2)+110(2)\ge600 \\ 440+220\ge600 \\ 620\ge600\: True! \end{gathered}`

Then Yes