Carolyn makes and sells necklaces. the material to make each necklace costs
$3.20. last week she made 12 necklaces and wants to make a total profit of $54.
using the equation 12(x+3.20)=54, carolyn determined that she will make a profit of $7.70 on each necklace. which error did carolyn make?
a. the solution is the amount she should sell each necklace for, and she will make a profit of $4.50 on each necklace.
b. she should have used the equation 12(x+3.20)=54 and found that she will make a profit of $1.30 on each necklace.
c. she should have used the equation x=54-12(3.20) and found that she will make a profit of $12.40 on each necklace.
d. the solution is the amount that it costs to make each necklace, and she should add $3.20 to find that she will make a profit of $10.90 on each necklace.

A. The solution is the amount she should sell each necklace for, and she will make a profit of $4.50 on each necklace.

Step-by-step explanation:

Let x be the cost of each necklace.  She needs to subtract the cost of the materials from each necklace to get the profit.

x-3.20 is the profit on each necklace.

She sells 12 necklaces

12* (x-3.20) = 54

Divide each side by 12

12/12* (x-3.20) = 54/12

x-3.20 = 4.50

Add 3.20 to each side

x-3.20 +3.20 = 4.50 +3.20

x = 7.70

She sells the necklaces for 7.70 and makes a 4.50 profit on each necklace

The correct answer is option A

The solution is the amount she should sell each necklace for, and she will make a profit of $4.50 on each necklace.

Step-by-step explanation:

It is given that,

The material to make each necklace costs  $3.20. Last week she made 12 necklaces and wants to make a total profit of $54.

To find the selling price of necklace

Let x be the profit on each necklace.

The we can write,

12(x - 3.20)=54

x - 3.20 = 54/12 = 4.5

x = 4.5 + 3.20 = 7.7

From this we get,

the amount she should sell each necklace  =  $7.7

And she will make a profit of $4.50 on each necklace.

The correct answer is Option A.

just sum

10 + 10 = 20

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places