Answer:
0.9 lb
Step-by-step explanation:
Let W be the weight of the cooking oil alone when the bottle is full.
Let E be the weight of the empty bottle
When the bottle is 1/5 full, the total weight is 1.5 lbs
That means 1/5 of the weight of cooking oil + weight of empty bottle = 1.5 lbs
We can write this as the following equation:
[tex]\dfrac{1}{5}W + E = 1.5 \dots\dots\dots[1][/tex]
Similarly we can form another equation for the second case when the bottle is 4/5 th full:
[tex]\dfrac{4}{5}W + E = 3.3 \dots\dots\dots[2][/tex]
Subtract equation [1] from equation [2] to give:
[tex]\dfrac{4}{5}W + E = 3.3\\\\-\\\\\dfrac{1}{5}W + E = 1.5[/tex]
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[tex]\dfrac{3}{5}W + 0 = 1.8[/tex]
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This gives us
[tex]\dfrac{3}{5}W = 1.8\\\\W = \dfrac{5}{3} \cdot 1.8\\\\W = 3.0\\[/tex]
Substitute for W = 3 in either equation and solve for E
Substituting for W in equation [1] we get
[tex]\\\\0.6 + E = 1.5\\\\E = 1.5 - 0.6\\\\E = 0.9[/tex]
Therefore the weight of the empty bottle is 0.9 lb
