As the owner of a banquet hall, you are in charge of catering a wedding reception. There are two dinners: a vegetarian dish that costs $16 per serving, and a chicken dish that costs $18 per serving. The 300 wedding guests have ordered their meals in advance, and the total cost of the food is $5256. How many of each type of dinner are you preparing?
How do I solve for the variables V and C?
use the number of dinners and the cost of the dinners.
v+c = 300
16v+18c = 5256
now solve as usual
To solve for the variables V and C, which represent the number of vegetarian and chicken dinners respectively, you can set up a system of equations based on the given information.
Let's assume that there are V vegetarian dinners and C chicken dinners.
1) The first equation is based on the total number of dinners:
V + C = 300
2) The second equation is based on the total cost of the food:
16V + 18C = 5256
To find the values of V and C, you can solve this system of equations simultaneously.
One method to solve the system is substitution. Solve equation 1 for V and substitute it into equation 2:
From equation 1, V = 300 - C
Substituting this value into equation 2:
16(300 - C) + 18C = 5256
Expanding and simplifying the equation:
4800 - 16C + 18C = 5256
Combining like terms:
2C = 456
Divide both sides by 2:
C = 228
Substitute the value of C back into equation 1 to find V:
V + 228 = 300
V = 300 - 228
V = 72
So, you would prepare 72 vegetarian dinners and 228 chicken dinners for the wedding reception.
To solve for the variables V (number of vegetarian dinners) and C (number of chicken dinners), we can use a system of equations.
Let's assume that there are V vegetarian dinners and C chicken dinners.
From the given information, we know that the total number of dinners is 300, so we can write the equation:
V + C = 300 ----(Equation 1)
We also know the total cost of the food is $5256. The cost of each vegetarian dinner is $16, and the cost of each chicken dinner is $18. Multiplying the cost by the number of dinners, we get the equation:
16V + 18C = 5256 ----(Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (V and C). We can solve this system to find the values of V and C.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution here.
From Equation 1, we can express V in terms of C by rearranging the equation:
V = 300 - C
Now substitute this value of V into Equation 2:
16(300 - C) + 18C = 5256
Expand and simplify this equation:
4800 - 16C + 18C = 5256
2C = 456
C = 228
Now we have found the value of C, which represents the number of chicken dinners. To find the number of vegetarian dinners (V), substitute this value of C back into Equation 1:
V + 228 = 300
V = 300 - 228
V = 72
Thus, you need to prepare 72 vegetarian dinners and 228 chicken dinners for the wedding reception.