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? Is the answer 125 for child and 125 for adult is this correct?
250=C+A
3.5C+7A=1347.50
3.5(250-A)+7A=
3.5A=472.5
A= 135
check my work
To find out the number of child and adult plates served at the St. Mark's Community Barbecue, we can set up a system of equations.
Let's assume the number of child's plates served as "C" and the number of adult's plates served as "A".
From the information given, we can form the following equations:
1. The total number of plates served is 250:
C + A = 250
2. The total amount collected is $1347.50:
(3.50 * C) + (7.00 * A) = 1347.50
To solve this system of equations, we can use substitution or elimination.
Let's use elimination to solve the equations:
Multiply the first equation by 7.00 to match the coefficient of "A" in the second equation:
7.00 * (C + A) = 7.00 * 250
7C + 7A = 1750
Now we can subtract the new first equation from the second equation:
(3.50 * C) + (7.00 * A) - (7C + 7A) = 1347.50 - 1750
3.50C = -402.50
Divide both sides by 3.50:
C = -402.50 / 3.50
C ≈ 115
By substituting the value of C back into the first equation, we can find the value of A:
115 + A = 250
A = 250 - 115
A = 135
Therefore, the correct answer is 115 child plates and 135 adult plates were served at the St. Mark's Community Barbecue.