At a butcher shop, 1 pound of beef and 2 pounds of chicken costs 859 cents. 1 pound of beef and 2 pounds of duck costs 951 cents. What is the total cost of 1 pound of beef, 1 pound of chicken, and 1 pound of duck (in cents)?
b + 2c = 859¢
b + 2d = 951¢
b + c + d = ((b + 2c) + (b + 2d))/2
To find the total cost of 1 pound of beef, 1 pound of chicken, and 1 pound of duck, we need to determine the individual prices of beef, chicken, and duck.
Let's assign variables to represent the prices:
- Let's call the price of 1 pound of beef 'B'.
- Let's call the price of 1 pound of chicken 'C'.
- Let's call the price of 1 pound of duck 'D'.
From the given information, we have two equations:
1) 1B + 2C = 859 (equation 1)
2) 1B + 2D = 951 (equation 2)
We need to solve these equations to find the individual prices of beef, chicken, and duck.
To solve this system of equations, we can use the method of substitution or elimination:
Let's start by solving it using the method of substitution.
From equation 1, we can isolate B:
1B = 859 - 2C
B = 859 - 2C (equation 3)
Now, let's substitute equation 3 into equation 2:
859 - 2C + 2D = 951
Simplifying the equation:
2D - 2C = 92
D - C = 46 (equation 4)
Now we have a new equation (equation 4) from which we can isolate D in terms of C.
D = C + 46 (equation 5)
Since we have an equation (equation 5) that relates D to C, we can substitute this into equation 3 to get the value of B.
B = 859 - 2C (equation 3)
= 859 - 2(C + 46) (Substituting equation 5 into equation 3)
= 859 - 2C - 92
= 767 - 2C (equation 6)
Now we have expressions for B, C, and D in terms of the variable C:
B = 767 - 2C (equation 6)
C = C (equation 7)
D = C + 46 (equation 5)
To find the total cost of 1 pound of beef, 1 pound of chicken, and 1 pound of duck, we can add their individual prices together:
Total Cost = B + C + D
= (767 - 2C) + C + (C + 46)
= 767 - 2C + C + C + 46
= 767 + 46
= 813 cents
Therefore, the total cost of 1 pound of beef, 1 pound of chicken, and 1 pound of duck is 813 cents.