19. an event space has a hall that can hold up to 250 people. the price for a party includes the cost of the…

19. an event space has a hall that can hold up to 250 people. the price for a party includes the cost of the room rental plus the cost of a meal for each guest. the event space advertises their prices for parties of 50 and 150. marissa’s parents are planning a quinceañera for 85 people. they budgeted $1,200. will it be enough? box in the final answer.\nmarissa’s quinceañera\ntotal cost ($)

19. an event space has a hall that can hold up to 250 people. the price for a party includes the cost of the room rental plus the cost of a meal for each guest. the event space advertises their prices for parties of 50 and 150. marissa’s parents are planning a quinceañera for 85 people. they budgeted $1,200. will it be enough? box in the final answer.\nmarissa’s quinceañera\ntotal cost ($)

Answer

Explanation:

Step1: Find cost - per - person increase

The cost for 50 people is $725 and for 100 people is $1325. The increase in number of people is $100 - 50=50$, and the increase in cost is $1325 - 725 = 600$. The cost per person is $\frac{600}{50}=12$.

Step2: Find fixed cost

Let the fixed cost (room rental) be $b$ and cost per person be $m$. For 50 people, the cost equation is $C = b+50m$. Substituting $m = 12$ and $C = 725$, we get $725=b + 50\times12$. $725=b + 600$, so $b=725 - 600=125$.

Step3: Calculate cost for 85 people

The cost formula is $C=b+nm$, where $n = 85$, $b = 125$ and $m = 12$. $C=125+85\times12=125 + 1020=1145$.

Answer:

Yes, it will be enough since the cost for 85 people is $1145 and the budget is $1200.