We need to purchase 4 packs of pencils and 4 packs of pens.
A pack of pencils costs $3. This means that to purchase four packs, we can multiply the cost of one pack by the number of packs we want to purchase.
$3.00 + $3.00 + $3.00 + $3.00 = $12.00
![3*4=12](https://img.qammunity.org/2023/formulas/mathematics/high-school/fex9im2iduq114w9gncre28y6rzaq5c8kj.png)
However, the distributive property can be completed by using the formula a(b + c), where a is the factor you want to multiply both by.
Since a pack of pencils is $3 and a pack of pens is $5, we can create an expression where a is 4 (this is the amount of packs we want for both pens and pencils), and b and c are the price of a pack of pencils and the price of a pack of pens.
![4(3+5)](https://img.qammunity.org/2023/formulas/mathematics/high-school/950kcjga55hp91ab31rfedj4v8gdmrfx7a.png)
Then, we will use the distributive property, which states that a(b + c) equals ab + ac. This means we multiply a and b and add the product of a and c to it.
![\begin{gathered} 4*3=12 \\ 4*5=20 \\ 12+20=32 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ltqi9lccyt9vph6h01jpo7d0zn70bwzg8i.png)
Therefore, to purchase 4 packs of pencils and 4 packs of pens, it will cost $32. Let's check our work:
![\begin{gathered} 3+3+3+3=12 \\ 5+5+5+5=20 \\ 12+20=32 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/s8f7fjybzc1bfipgpre0rldnxwjay5fynj.png)
We still reach 32 dollars, so the final answer is $32. This is determined with 4(3 + 5).