Answer :
To find the number of cubic feet occupied by 195 lb of water, we use the given weight per cubic foot of water. Here is the step-by-step solution:
1. The weight of water per cubic foot is
$$62 \frac{1}{2} \text{ lb} = 62.5 \text{ lb}.$$
2. Let the volume (in cubic feet) occupied by the water be $V$. Since 195 lb of water is given, we set up the equation:
$$V = \frac{\text{total weight of water}}{\text{weight per cubic foot}} = \frac{195}{62.5}.$$
3. To express $62.5$ as a fraction, note that:
$$62.5 = \frac{125}{2}.$$
Thus, the volume becomes:
$$V = \frac{195}{\frac{125}{2}} = 195 \times \frac{2}{125} = \frac{390}{125}.$$
4. Simplify the fraction $\frac{390}{125}$ by dividing the numerator and denominator by 5:
$$\frac{390}{125} = \frac{390 \div 5}{125 \div 5} = \frac{78}{25}.$$
5. To express $\frac{78}{25}$ as a mixed numeral, perform the division:
- Divide 78 by 25. The quotient is 3, since $3 \times 25 = 75$.
- The remainder is $78 - 75 = 3$, so the fractional part is $\frac{3}{25}$.
Thus,
$$\frac{78}{25} = 3 \frac{3}{25}.$$
Therefore, 195 lb of water occupies
$$3 \frac{3}{25}$$
cubic feet.
1. The weight of water per cubic foot is
$$62 \frac{1}{2} \text{ lb} = 62.5 \text{ lb}.$$
2. Let the volume (in cubic feet) occupied by the water be $V$. Since 195 lb of water is given, we set up the equation:
$$V = \frac{\text{total weight of water}}{\text{weight per cubic foot}} = \frac{195}{62.5}.$$
3. To express $62.5$ as a fraction, note that:
$$62.5 = \frac{125}{2}.$$
Thus, the volume becomes:
$$V = \frac{195}{\frac{125}{2}} = 195 \times \frac{2}{125} = \frac{390}{125}.$$
4. Simplify the fraction $\frac{390}{125}$ by dividing the numerator and denominator by 5:
$$\frac{390}{125} = \frac{390 \div 5}{125 \div 5} = \frac{78}{25}.$$
5. To express $\frac{78}{25}$ as a mixed numeral, perform the division:
- Divide 78 by 25. The quotient is 3, since $3 \times 25 = 75$.
- The remainder is $78 - 75 = 3$, so the fractional part is $\frac{3}{25}$.
Thus,
$$\frac{78}{25} = 3 \frac{3}{25}.$$
Therefore, 195 lb of water occupies
$$3 \frac{3}{25}$$
cubic feet.
