Question 13 (Essay Worth 12 points)

(Translating Algebraic Expressions HC)

A farmer earns [tex]$[ \text{amount per orange} ] for each orange she sells. She had to pay $[/tex][ \text{amount for fertilizer} ] for fertilizer.

Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, [tex]n[/tex]. Make sure the values you choose make sense for this situation. (6 points)

Part B: Write an algebraic expression from your written description used in Part A. Let [tex]n[/tex] stand for the number of oranges. (6 points)



Answer :

### Part A: Rewritten Description

Let's assume the farmer earns [tex]$2 for each orange she sells and has to pay $[/tex]50 for fertilizer.

So, for any number of oranges [tex]\( n \)[/tex]:

1. Earnings from selling oranges: If the farmer sells [tex]\( n \)[/tex] oranges, she earns [tex]$2 per orange. Thus, if she sells \( n \) oranges, her total earnings are \( 2n \) dollars. 2. Cost of fertilizer: The farmer needs to pay $[/tex]50 for fertilizer. This is a constant cost regardless of the number of oranges sold.

3. Net earnings: The net amount of money the farmer earns is determined by subtracting the fertilizer cost from her earnings. Therefore, her net earnings after paying for fertilizer would be [tex]\( 2n - 50 \)[/tex] dollars.

In summary, if the farmer sells [tex]\( n \)[/tex] oranges, she will earn a total of [tex]$2 per orange, but after paying $[/tex]50 for fertilizer, her net earnings will be [tex]\( 2n - 50 \)[/tex] dollars.

### Part B: Algebraic Expression

Based on the description in Part A, we can write the algebraic expression for the farmer's net earnings.

- Let [tex]\( n \)[/tex] represent the number of oranges sold.
- The earning per orange is [tex]$2, thus the total earnings from selling \( n \) oranges is \( 2n \). - The fertilizer cost is $[/tex]50, a constant value.

The algebraic expression for the farmer's net earnings after paying for the fertilizer is:

[tex]\[ 2n - 50 \][/tex]

This algebraic expression can now be used to calculate the net earnings for the farmer for any given number of oranges [tex]\( n \)[/tex] she sells.