Question

A mover packs books, CDs, and DVDs into a moving box. If the box contains 6.5 kg of books, 1.5 kg of CDs, and 2.0 kg of DVDs, what is the percent by mass of each object in the box? Books: % of the mass CDs: % of the mass DVDs: % of the mass

Answer 1

`\%_(books)=65\%\\\%_(CDs)=15\%\\\%_(DVDs)=20\%`

Step-by-step explanation:

We should firstly define the equation that we'll be using for the purpose of this problem. Percent by mass is defined as the ratio between the mass of a component (such as books, CDs or DVDs in this case) divided by the total mass of the pack multiplied by 100 %:

`\%_(mass)=(m_c)/(m_t)\cdot 100\%`

Here
`m_c` is the mass of a component;

`m_t` is the total mass (of the pack).

Firstly, let's find the total mass of the pack summing all the individual masses present:

`m_t=m_(books)+m_(CDs)+m_(DVDs)=6.5 kg+1.5 kg+2.0 kg=10.0 kg`

Now, we have a total of 3 components. Let's firstly apply the equation for books:

`\%_(books)=(m_(books))/(m_(total))\cdot 100\%=(6.5 kg)/(10.0 kg)\cdot 100\%=65 \%`

Similarly, find the percent by mass of CDs:

`\%_(CDs)=(m_(CDs))/(m_(total))\cdot 100\%=(1.5 kg)/(10.0 kg)\cdot 100\%=15 \%`

Finally, find the percent by mass of DVDs:

`\%_(DVDs)=(m_(DVDs))/(m_(total))\cdot 100\%=(2.0 kg)/(10.0 kg)\cdot 100\%=20\%`