Question

$\frac{9}{2}L\text{of juice is packed into identical bottles.}\text{If each bottle has a maximum capacity of}1\frac{3}{4}L,\text{calculate the minimum number of}\text{bottles required to pack all the juice.}$

• A. 1 bottle
• B. 4 bottles
• C. 2 bottles
• D. 3 bottles

Answer 1

The correct option is D 3 bottles

$\text{Total volume of juice}=\frac{9}{2}L$

$\text{Capacity of each bottle}=1\frac{3}{4}L=\frac{(4\times 1)+3}{4}=\frac{7}{4}L$

$\text{Number of bottles required}\text{Total volume of juice}=÷\text{Capacity of each bottle}$

$=\frac{9}{2}L÷\frac{7}{4}L$

$\text{Calculating}\frac{9}{2}÷\frac{7}{4}\text{using the}keep-change-flip\text{method, we get:}$


$\text{Calculating}\frac{9}{2}\times \frac{4}{7}\text{, we get:}$

$\frac{9}{2}\times \frac{4}{7}=\frac{9\times 4}{2\times 7}=\frac{36}{14}=\frac{18}{7}=2\frac{4}{7}$

$\therefore \text{To pack the all of the juice, we need 2}\text{entire bottles as well as}\frac{4}{7}\text{th of a third}\text{bottle}.$

$\text{Hence, at least 3 bottles are required to}\text{pack all the juice.}$