Question

Cesar is planning a $4$-day trip to visit his friend at a college in another state. It will cost him $\backslash (198$for airfare, $\backslash )56$for local transportation, and $\backslash (45$per day for food. He has $\backslash )189$in savings and can earn $\$35$for each lawn he mows. How many lawns must he mow to have enough money to pay for the trip?

Short answer

The number of lawns Cesar must mow is $6$.

Step-by-step solution

Step 1. Given Information 

We are given that savings of Cesar is $\$189$and he earns $\$35$for each lawn he mows .

We have to find the number of lawns he must mow to have enough money to pay for the trip.

Step 2. Forming the inequality

The total expenses will be,

$$\begin{gathered} =\$198+\$56+\$45\times 4 \\ =\$434 \end{gathered}$$

Let the number of lawns mowed be x,

Since, the total expense is $\$434$. Therefore, sum of earnings and savings should be greater than or equal to $\$434$, so the inequality will be,

localid="1647274784944" $35x+189\ge 434$

Step 3. Solving the Inequality 

Subtracting $189$from both sides, we get

role="math" localid="1647274728563" $$\begin{gathered} 35x\ge 434-189 \\ 35x\ge 245 \\ x\ge \frac{245}{35} \\ x\ge 5.44 \end{gathered}$$

The number of lawns must be whole numbers, so

$x=6$

He must mow $6$ lawns to have enough money to pay for the trip.