Ms. Higdon is planning her wedding. One venue charges

10,000 plus 25 dollars per person, while another venue simply

charges 150 dollars per person. How many people would need

to attend for the venues to cost the same amount?

80 people would need to attend for the venues to cost the same amount.

Step-by-step explanation:

Let the total number of people who attend the wedding = m

The venue charges of venue 1 = $10,000

The per person charge of Venue 1 = $25 per person

So, the charge for m people = m x ($25) = 25 m

So, The total charge of Venue 1 = Venue Charge + People Cost

= $10, 000 + 25 m

Now, The per person charge of Venue 2 = $150 per person

So, the charge for m people = m x ($150) = 150 m

So, The total charge of Venue 2 = 150 m

According to question:

For m people both charges are equal ⇒ $10, 000 + 25 m = 150 m

or, 10,000 = 150 m - 25 m

⇒ 125 m = 10,000

⇒ m = 10,000 / 125 = 80

or, m = 80

Hence, 80 people would need to attend for the venues to cost the same amount.