Question

Carolyn makes and sells necklaces. The material to make each necklace costs $3. 20. She has 12 necklaces to sell and wants to make a total profit of $54. The following equation describes the situation. 12 (x minus 3. 20) = 54 Carolyn found that x = 7. 7 and determined that she will make a profit of $7. 70 on each necklace. Which error did Carolyn make? The solution means that she should charge $7. 70 for each necklace. The solution means that each necklace costs $7. 70 to make. The solution to the equation is not x = 7. 7. Carolyn did not distribute the parentheses when solving.

Answer 1

Answer:

The solution means that she should charge $7.70 for each necklace

Step-by-step explanation:

$12(x-3.20)=54\\\\\implies 12x-38.4=54\\\\\implies 12x=92.4\\\\\implies x=7.7$

The solution means that she should charge $7.70 for each necklace.

She will make a profit of $4.50 for each necklace.

12 x $4.50 = $54

Answer 2

Error made by Carolyn is that she thought, profit of selling 12 necklaces is $7.70, but it was the selling price of necklace.

What is linear equation?

Linear equation is the equation in which the highest power of the unknown variable is one.

Here, in the problem, it is given that the material to make each necklace costs $3.20.

Carolyn has 12 necklaces to sell and wants to make a total profit of $54.

Suppose the selling price of each necklace is x dollars. As the total cost of one necklace is $3.20. Thus the total profit earn on selling one neck less is,

$P=x-3.20$

Now Carolyn has 12 necklaces to sell and wants to make a total profit of $54. Thus, multiply the profit of one necklace with 12 and equate it with 54 as,.

$12(x-3.20)=54$

This is the equation, which best describe the situation.

Solve for x as,

$(x-3.20)=\dfrac{54}{12}\\x=4.5+3.2\\x=7.70$

The selling price must be $7.70.

Thus the error made by Carolyn is that she place the thought, that the profit of selling 12 necklaces is $7.70, but it was the selling price of necklace.

Learn more about the linear equation here;

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