Question

Or

A charity is considering the possibility of having a benefit night at two different restaurants. The owner of the local Italian restaurant has offered to make a donation of $200 and $3 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $100 plus $4 per diner. Based on the number of diners who have promised to participate in the event, it appears that each restaurant would donate the same total amount. How much would each restaurant donate?

Answer 1

number of diners for the benefit night is x

Italian restaurant the donation is $200 plus $3 / diner:

200 + 3x

mexican restaurant the donation is $100 plus $4 / diner:

100 + 4x

both restaurants are donating the same amount:

200 + 3x = 100 + 4x

solve x:

x = 100

italian restaurant: 200 + 3(100) = $500

mexican restaurant: 100 + 4(100) = $500

each restaurant would donate = $500

Answer 2

$300$ and $500$

Explanation:

Let x be the number of diners at each restaurant.

The Italian restaurant would donate $200 + $3x$, and the Mexican restaurant would donate $100 + $4x$. Since the total donation from each restaurant is the same, we can set up an equation and solve for $x$:

$200 + 3x = 100 + 4x$

$x = 100$

The Italian restaurant would donate $200 + $3 * 100 = $300$.

The Mexican restaurant would donate $100 + $4 * 100 = $500$.

Therefore, each restaurant would donate $300$ and $500$, respectively.