Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
large pitcher --- x
small pitcher --- y
x + 2y = 8
x - y = 2
subtract them:
3y = 6
y = 2
then x = 4
large holds 4 cups, the smaller holds 2 cups
Let's assume the capacity of each small pitcher is represented by the variable "S", and the capacity of the large pitcher is represented by the variable "L".
From the given information, we can create two equations:
1) 2S + L = 8 (Equation 1)
(The total capacity of two small pitchers and one large pitcher is 8 cups)
2) L - S = 2 (Equation 2)
(The capacity of one large pitcher minus one small pitcher is 2 cups)
To solve this system of equations, we can use the method of substitution.
Rearrange Equation 2 to solve for L in terms of S:
L = S + 2
Now substitute this expression for L in Equation 1:
2S + (S + 2) = 8
Simplify the equation:
2S + S + 2 = 8
3S + 2 = 8
Subtract 2 from both sides:
3S = 6
Divide both sides by 3:
S = 2
Now substitute the value of S back into Equation 2 to find the capacity of the large pitcher (L):
L - 2 = 2
L = 4
Therefore, each small pitcher can hold 2 cups of water, and the large pitcher can hold 4 cups of water.
To solve this problem, we need to set up a system of equations.
Let's first assign variables to the unknown quantities:
Let's call the capacity of one small pitcher as 'S' (in cups)
Let's call the capacity of one large pitcher as 'L' (in cups)
From the given information, we can form two equations:
Equation 1: Two small pitchers and one large pitcher can hold 8 cups of water.
2S + L = 8
Equation 2: One large pitcher minus one small pitcher constitutes 2 cups of water.
L - S = 2
Now we can solve this system of equations to find the values of S and L.
Let's rearrange Equation 2 to express L in terms of S:
L = S + 2
Substitute this value of L in Equation 1:
2S + S + 2 = 8
3S + 2 = 8
3S = 6
S = 2 (capacity of one small pitcher)
Now, substitute this value of S into Equation 2 to get the value of L:
L - 2 = 2
L = 4 (capacity of one large pitcher)
Therefore, each small pitcher can hold 2 cups of water, and the large pitcher can hold 4 cups of water.