Two restaurants have rooms to rent for dinner parties. One restaurant charges $100 to rent a room and $20 per person. The other restaurant charges $25 to rent the room and $25 per person. Which of the following is the number of people for which the cost of a dinner party would be the same at both restaurants?
A. 10
B. 15
C. 20
D. 25
Dear Roberta,
Let the number of people be y
100 + 20y = 25 + 25 y
75 = 5y
y = 15
So the answer should be B
Hope it helps!
Wishing you the best of luck,
Barry
n = numbers of persons
100 + 20 * n = 25 + 25 * n
100 + 20 n = 25 + 25 n Subtract 25 to both sides
100 + 20 n - 25 = 25 + 25 n - 25
75 + 20 n = 25 n Subtract 20 n to both sides
75 + 20 n - 20 n = 25 n - 20 n
75 = 5 n Divide both sides by 5
75 / 5 = 5 n / 5
15 = n
n = 15
Proof:
100 + 20 * 15 = 25 + 15 * 25
100 + 300 = 25 + 375
400 $ = 400 $
ppizzazz
To find the number of people for which the cost of a dinner party would be the same at both restaurants, we need to set up an equation and solve for the variable.
Let's represent the number of people as 'x'.
For the first restaurant, the total cost would be the room rental fee of $100 plus $20 per person.
Total cost at the first restaurant = $100 + ($20 * x) = $100 + $20x
For the second restaurant, the total cost would be the room rental fee of $25 plus $25 per person.
Total cost at the second restaurant = $25 + ($25 * x) = $25 + $25x
Setting the two equations equal to each other, we have:
$100 + $20x = $25 + $25x
To solve for 'x', start by isolating the terms with 'x'.
$20x - $25x = $25 - $100
-$5x = -$75
Dividing both sides by -5:
x = 15
Therefore, the number of people for which the cost of a dinner party would be the same at both restaurants is 15.
So, the answer is B. 15.