A and B weigh 156 pounds. A and C weigh 171 pounds. How much do they each weigh if the total weight is 255 pounds?
a=72
b=84
c=99
To find the weight of A, B, and C individually, we can set up a system of equations:
Let's represent the weight of A as 'x', B as 'y', and C as 'z'.
From the given information, we can write the following equations:
Equation 1: x + y = 156 (A and B weigh 156 pounds)
Equation 2: x + z = 171 (A and C weigh 171 pounds)
Equation 3: x + y + z = 255 (total weight is 255 pounds)
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
From Equation 1, we can express y in terms of x: y = 156 - x.
Substituting this expression into Equation 3, we get:
x + (156 - x) + z = 255.
156 + z = 255.
z = 255 - 156.
z = 99.
Substituting the value of z into Equation 2, we have:
x + 99 = 171.
x = 171 - 99.
x = 72.
So, A weighs 72 pounds, B weighs 156 - 72 = 84 pounds, and C weighs 99 pounds.
Method 2: Elimination
By subtracting Equation 1 from Equation 2, we can eliminate x:
(x + z) - (x + y) = 171 - 156.
z - y = 15.
Next, we add Equation 1, Equation 2, and Equation 3:
(x + y) + (x + z) + (x + y + z) = 156 + 171 + 255.
3x + 2y + 2z = 582.
Simplifying, we have:
2z - 2y = 15,
3x + 2y + 2z = 582.
Adding these two equations eliminates y and z:
3x + 2z = 582,
3x + 2z = 582.
Now, we solve this system:
3x + 2z = 582.
3x + 2z = 582.
Since both equations are identical, we can't determine unique solutions for x, y, and z using this method.
Therefore, we proceed with the Substitution method.
Using the values obtained from the Substitution method:
A weighs 72 pounds, B weighs 84 pounds, and C weighs 99 pounds.