Question

In the following exercises, solve.

Wedding Budget Adele and Walter found the perfect venue for their wedding reception. The cost is $\backslash (9,850$for up to $100$guests, plus $\backslash )38$for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than $\$12,500$?

Short answer

The total guests attend the weeding reception under the budget is $169$.

Step-by-step solution

Step 1. Given Information 

We are given that the total budget of Adele and Walter is $\$12,500$and the cost is $\$9850$for hundered guests plus $\$38$for each additional guest.

We have to find the number of guest attend the wedding within the budget.

Step 2. Forming the inequality 

Let the number of guests bex,

The total budget is $\$12,500$,

So, the inequality will be

$38x+9850\le 12,500$

Step 3. Solving the Inequality  

Subtracting$9850$from both sides, we get

localid="1647329894488" $$\begin{gathered} 38x+9850\le 12,500 \\ 38x\le 12,500-9,850 \\ 38x\le 2650 \end{gathered}$$

Dividing by $38$, we get

localid="1647330064901" $$\begin{gathered} x\ge \frac{2650}{38} \\ x\le 69.73 \end{gathered}$$

The number of guests must be a whole number, so

$x=69$

Hence, the total guests is $100+69=169$.