Question

16. An empty jar has a volume of8x^2 + 2x - 4 cubic inches. Josh pours4x^2 – 3x +2 cubic inches of waterinto the jar. How many more cubicinches of water could the jar stillhold?

Answer 1

The total volume of the jar is (in cubic inches):

`V=8x^2+2x-4`

Josh pours inside the jar a volume of water (in cubic inches):

`V_0=4x^2-3x+2`

After Josh pours inside the jar a volume of water V0 (in cubic inches), the jar will still hold a volume equal to the difference between the total volume V and the volume of water poured V0:

`\begin{gathered} V^(\prime)=V-V_0 \\ V^(\prime)=(8x^2+2x-4)-(4x^2-3x+2) \\ V^(\prime)=8x^2-4x^2+2x+3x-4-2 \\ V^(\prime)=4x^2+5x-6 \end{gathered}`

Answer: 4x² + 5x - 6