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.