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What equation could be used to represent the verbal representation below?

Sanita wants to sell his artwork at a local fair. He has created 10 pieces of artwork and has spent [tex]$44 in creating them. He wants to make a profit of $[/tex]300 at the fair. What is the price he needs to sell each piece to make that profit?

A. 10a = 300 - 44
B. 10a = 300
C. 10a = 44
D. 10a = 44 + 300


Sagot :

Sure, let's solve the problem step-by-step:

1. Determine Total Costs and Profit Goals:
- Sanita has already spent [tex]\( \$44 \)[/tex] on creating the artwork.
- Sanita wants to make a profit of [tex]\( \$300 \)[/tex].

2. Calculate the Total Amount Sanita Needs to Earn:
- To cover his costs and achieve his profit goal, we need to sum the incurred costs and the desired profit:
[tex]\[ \text{Total amount needed} = \$44 + \$300 = \$344 \][/tex]

3. Number of Pieces Created:
- Sanita has created a total of 10 pieces of artwork.

4. Find the Price Per Piece:
- To find out the price at which he needs to sell each piece to meet his goal, we can set up the equation:
[tex]\[ 10a = 344 \][/tex]
where [tex]\( a \)[/tex] represents the price per piece.

5. Logical Representation in Equation Form:
- The correct mathematical representation of the given problem is:
[tex]\[ 10a = 44 + 300 \][/tex]

From the given options, the correct equation is:
[tex]\[ 10a = 44 + 300 \][/tex]