A glass is filled with water and the total weight is 220g. If the glass is halffilled with water, the total weight is 120g. What is the net weight of the glass?
There may be a logic way of doing it but the following is the longer "math" way.
G = weight of the glass
W = weight of the water.
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G + W = 220
G + 1/2(W) = 120
Two equations in two unknowns. Solve for G (and W if desired).
Post your work if you get stuck.
To find the net weight of the glass, let's solve the system of equations using the substitution method.
We are given two equations:
1) G + W = 220 (Equation 1)
2) G + 1/2(W) = 120 (Equation 2)
First, let's solve Equation 2 for G:
G + 1/2(W) = 120
G = 120 - 1/2(W)
Now substitute this value of G into Equation 1:
(120 - 1/2W) + W = 220
120 + 1/2W + W = 220
3/2W = 220 - 120
3/2W = 100
To simplify the equation, multiply both sides by 2/3:
W = (100)(2/3)
W = 200/3
W ≈ 66.67 g
Now substitute this value of W back into Equation 1 to find G:
G + (200/3) ≈ 220
G ≈ 220 - (200/3)
G ≈ 660/3 - 200/3
G ≈ 460/3
G ≈ 153.33 g
The net weight of the glass is approximately 153.33 g.