Question

In the following exercises, solve.

Eun-Kyung works as a tutor and earns $\backslash (60$per hour. She has $\backslash )792$in savings. She is planning an anniversary party for her parents. She would like to invite $40$guests. The party will cost her $\backslash (1,520$for food and drinks and $\backslash )150$for the photographer. She will also have a favor for each of the guests, and each favor will cost $\$7.50$. How many hours must she tutor to have enough money for the party?

Short answer

Eun-Kyung must tutor$20$hours for enough money for the party.

Step-by-step solution

Step 1. Given Information 

We are given that Eun-Kyung savings is $\$792$and she earn $\$60$per hour for tutoring.

We have to find the number of hours she must tutor to have enough money for the party.

Step 2. Forming the inequality 

The total expenses will be,

$$\begin{gathered} =\$1520+\$150+\$7.5\times 40 \\ =\$1970 \end{gathered}$$

Let the number of hours tutored be x,

Since, the total expense is $\$1970$. so, the sum of earnings and savings should be greater than or equal to $\$1970$.

So, the inequality will be,

$60x+792\ge 1970$

Step 3. Solving the Inequality  

Subtracting $792$from both sides, we get

localid="1647318938896" role="math" $$\begin{gathered} 60x+792\ge 1970 \\ 60x\ge 1970-792 \\ 60x\ge 1178 \\ x\ge \frac{1178}{60} \\ x\ge 19.6 \end{gathered}$$

Since, the number of hours must be whole numbers, so

localid="1647318923272" $x=20$

She must tutor$20$hours for enough money.