Question

In the following exercises, solve.

Five student government officers want to go to the state convention. It will cost them \($110$for registration, $\backslash )375$for transportation and food, and $\backslash (42$per person for the hotel. There is$\backslash )450$budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $$5$per car, how many cars must they wash in order to have enough money to pay for the trip?

Short answer

The number of cars students must wash is $49$.

Step-by-step solution

Step 1. Given Information

We are given that the budget is $450$and student wash cars at the rate of $5\$$per car.

We have to find the number of cars student must wash in order to have enough money to pay for the trip.

Step 2. Forming the inequality

The total expenses will be,

$$\begin{gathered} =\$110+\$375+\$42\times 5 \\ =\$695 \end{gathered}$$

Let the number of car washed be $x$,

Since, the total expense is $\$695$. so, the sum of their earning and saving should be greater than or equal to $\$695$.

localid="1647274747576" $5x+450\ge 695$

Step 3. Solving the Inequality 

Subtracting $450$from both sides, we get

localid="1647274765569" $$\begin{gathered} 5x\ge 695-450 \\ 5x\ge 245 \\ x\ge \frac{245}{5} \\ x\ge 49 \end{gathered}$$

Hence, the number of cars washed must be greater than or equal to $49$.