Question

In the following exercises, solve.

Shower Budget Penny is planning a baby shower for her daughter-in-law. The restaurant charges $\backslash (950$for up to $25$guests, plus $\backslash )31.95$for each additional guest. How many guests can attend if Penny wants the total cost to be no more than $\$1,500$?

Short answer

The total number of guests is $42$.

Step-by-step solution

Step 1. Given Information 

We are given that the restaurant charges $\$950$for up to $25$guests, plus $\$31.95$for each additional guest.

We have to find the number of number of guest attend within the Penny's budget.

Step 2. Forming the inequality 

Let the number of guests be x,

The total budget is $\$1,500$, So, the inequality will be

$31.95x+950\le 1,500$

Step 3. Solving the Inequality   

Subtracting $950$from both sides, we get

$$\begin{gathered} 31.95x+950\le 1,500 \\ 31.95x\le 1,500-950 \\ 31.95x\le 550 \\ x\ge \frac{550}{31.95} \\ x\le 17.21 \end{gathered}$$

The number of guests must be a whole number, so

$x=17$

So, the total guests will be$25+17=42$.