Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. 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 $625 and $5 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $449 plus $6 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? How many diners promised to participate? Each restaurant would donate $___ with __ diners promising to participate.

Answer 1

A. y = 625 + 5x ___(1)

y = 449 + 6x ___(2)

B. $1505 and 176 diners

C. Each restaurant will donate $1505 with 176 diners promising to participate.

Step-by-step explanation

Let the amount that each restaurant contributes be y.

Let the number of diners promising to participate be x.

For the Italian restaurant, we have that they will make a donation of $625 and $5 per diner that night. This means that:

y = 625 + 5 * x

=> y = 625 + 5x ______(1)

For the Mexican restaurant, we have that they will contribute $449 plus $6 per diner. This means that:

y = 449 + 6 * x

y = 449 + 6x ______(2)

Now, we have a system of equations:

y = 625 + 5x ___(1)

y = 449 + 6x ___(2)

Using substitution method, we will substitute the second equation into the first one. That is:

449 + 6x = 625 + 5x

Collect like terms:

6x - 5x = 625 - 449

x = 176 diners

To find the value of y, substitute this value of x into equation (1):

=> y = 625 + 5(176)

y = 625 + 880

y = $1505

Therefore, each restaurant will donate $1505 with 176 diners promising to participate.