Question

You have $1200 for your trip to the beach. You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare. Write an inequality that can be used to determine the maximum number of days you can stay at the beach. Clearly indicate what the variable represents. Then Solve the inequality, and interpret your answer in a complete sentence.

Answer 1

`\begin{gathered} 230+160\leq1200\rightarrow Inequality \\ 6\text{ days at Ma}\Xi mun \end{gathered}`

Step-by-step explanation

Step 1

let x represents the numbers of days you can stay at the beach

then,

You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.

so

`\text{total}=230+160x`

but, you have only $1200, so the total needs to be smaller or equal than 1200

`230+160x\leq1200\rightarrow Inequality`

Step 2

solve the inequality

`\begin{gathered} 230+160x\leq1200\rightarrow Inequality \\ subtract\text{ 230 in both sides} \\ 230+160x-230\leq1200-230 \\ 160x\leq970 \\ \text{divide both sides by 160} \\ (160x)/(160)\leq(970)/(160) \\ x\leq6.0625 \\ \text{rounded} \\ x\leq6 \end{gathered}`

it means you can stay maximum 6 days

I hope this helps you