To find the cost of one orange in cents when six dozen equally priced oranges cost a total of [tex]\( n \)[/tex] dollars, follow these steps:
1. Calculate the total number of oranges:
- There are 6 dozen oranges.
- Since there are 12 oranges in a dozen, the total number of oranges is:
[tex]\[
6 \times 12 = 72 \text{ oranges}
\][/tex]
2. Determine the cost of one orange in dollars:
- The total cost for 72 oranges is [tex]\( n \)[/tex] dollars.
- Therefore, the cost for one orange in dollars is:
[tex]\[
\frac{n}{72} \text{ dollars}
\][/tex]
3. Convert the cost from dollars to cents:
- There are 100 cents in a dollar.
- To convert the cost from dollars to cents, multiply the cost in dollars by 100:
[tex]\[
\left(\frac{n}{72}\right) \times 100
\][/tex]
4. Simplify the expression:
- Perform the multiplication:
[tex]\[
\frac{n \times 100}{72} = \frac{100n}{72}
\][/tex]
- Simplify the fraction:
[tex]\[
\frac{100n}{72} = \frac{25n}{18}
\][/tex]
Thus, the cost of one orange in cents is [tex]\(\frac{25n}{18}\)[/tex].
Therefore, the correct answer is:
[tex]\(\boxed{\frac{25n}{18}}\)[/tex]
