Question

question 5
mr. de beer is planning on storing food parcels in a storeroom. study the diagram below and answer the questions that follow.
note:
dimensions of storeroom: 6.5 m by 5 m
box dimensions and packaging options
option 1
5.1 how many boxes may be stored on the floor of the storeroom if mr. de beer uses option 1?
show all your calculations.
5.2 mr. de beer claims that he could pack more boxes on the floor of the storeroom if he used option 2.
verify his claim by means of calculations.

Explanation:

Step1: Calculate floor area of storeroom

The storeroom has dimensions 6.5m by 5m. The area of the storeroom floor $A_{s}$ is given by the formula $A = l\times w$, so $A_{s}=6.5\times5 = 32.5$ $m^{2}$.

Step2: Calculate area of a box in Option 1

For Option 1, the box has dimensions 1.2m by 0.7m. The area of a single - box $A_{b1}$ is $A_{b1}=1.2\times0.7 = 0.84$ $m^{2}$.

Step3: Calculate number of boxes in Option 1

The number of boxes $n_{1}$ that can be stored is $n_{1}=\lfloor\frac{A_{s}}{A_{b1}}
floor$, where $\lfloor x
floor$ is the floor function. So $n_{1}=\lfloor\frac{32.5}{0.84}
floor=\lfloor38.69
floor = 38$.

Step4: Calculate area of a box in Option 2

For Option 2, the box has dimensions 0.7m by 1.2m (same area as Option 1 since $0.7\times1.2 = 0.84$ $m^{2}$). The area of a single - box $A_{b2}=0.7\times1.2 = 0.84$ $m^{2}$.

Step5: Calculate number of boxes in Option 2

The number of boxes $n_{2}$ that can be stored is $n_{2}=\lfloor\frac{A_{s}}{A_{b2}}
floor$. So $n_{2}=\lfloor\frac{32.5}{0.84}
floor=\lfloor38.69
floor = 38$.

Answer:

5.1: 38
5.2: Mr. de Beer's claim is false. The number of boxes that can be stored using Option 1 is 38 and the number of boxes that can be stored using Option 2 is also 38. Since $n_{1}=n_{2} = 38$, he cannot pack more boxes using Option 2.