The St. Mark's Community Barbecue served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served

child's plate --- x

adult ----- 250-x

solve

3.5x + 7(250-x) = 1347.5

To determine the number of each type of plate served at the St. Mark's Community Barbecue, we can set up a system of linear equations. Let's use the following variables:

Let's assume the number of child's plates served is 'c' and the number of adult's plates served is 'a'.

From the given information, we know that:

1) The total number of plates served is 250: c + a = 250

2) The total amount collected is $1347.50: 3.50c + 7.00a = 1347.50

Now we can solve this system of equations to find the values of 'c' and 'a'.

First, let's solve equation 1 for 'c':

c = 250 - a

Now substitute this value of 'c' into equation 2:

3.50(250 - a) + 7.00a = 1347.50

875 - 3.50a + 7.00a = 1347.50

3.50a = 1347.50 - 875

3.50a = 472.50

a = 472.50 / 3.50

a ≈ 135

Substitute this value of 'a' back into equation 1 to find 'c':

c + 135 = 250

c = 250 - 135

c ≈ 115

Therefore, approximately 135 adult's plates and 115 child's plates were served at the St. Mark's Community Barbecue.