Question

In the following exercises, solve.

Alonzo works as a car detailer. He charges $\backslash (175$per car. He is planning to move out of his parents’ house and rent his first apartment. He will need to pay $\backslash )120$for application fees, $\backslash (950$for security deposit, and first and last months’ rent at $\backslash )1,140$per month. He has $\$1,810$in savings. How many cars must he detail to have enough money to rent the apartment?

Short answer

Alonzo must detail$9$cars to have enough money to rent the apartment.

Step-by-step solution

Step 1. Given Information 

We are given that the savings of Alonzo is $\$1,810$and he detail cars at the rate of $\$175$per car.

We have to find the number of cars he must detail to have enough money to rent the apartment.

Step 2. Forming the inequality 

The total expenses will be,

$$\begin{gathered} =\$120+\$950+\$1140\times 2 \\ =\$3350 \end{gathered}$$

Let the number of car detail be x,

Since, his total expense is $\$3350$.Therefore, sum of earnings and savings should be greater than or equal to $\$3350$.

So, the inequality will be,

$175x+1810\ge 3350$

Step 3. Solving the Inequality  

Subtracting $1180$from both sides, we get

$$\begin{gathered} 175x\ge 3350-1810 \\ x\ge \frac{1540}{175} \\ x\ge 8.8 \end{gathered}$$

Since, the number of cars must be whole numbers.

$x=9$

Hence, the number of cars Alonzo must detail is $9$.