Question

Carolyn makes and sells necklaces. The material to make each neckalce 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 - 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

This question tests the concept of application of algebra in a real world problem.

In algebra, we always first define what x is before we apply it in the equation.

Define x:

Let x be selling price of 1 necklace.

Find the earnings of 1 necklace:

$\text{Selling Price of 1 necklace}= x$

$\text{Cost Price of 1 necklace }= 3.20$

$\text{Profit} = x - 3.20$

Find the earnings of 12 necklaces:

$\text{Profit for 1 necklace}= x - 3.20$

$\text{Profit for 12 necklaces}= 12(x - 3.20)$

She wants to make a profit of $54:

$12( x - 3.20) = 54$

Solve the equation:

$12(x - 3.20) = 54$

$12x - 38.4= 54$

$12x = 54 + 38.4$

$12x = 92.4$

$x = 7.70$

Conclusion:

x was defined as the selling price of 1 necklace.

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

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

Answer 2

Answer:

Step-by-step explanation: