Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8(x+2.75)=78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make?

Rita's error is in the sign of 2.75 in her equation. If x is her selling price, Rita needs to find the value of x in
.. 8(x -2.75) = 78

That value will be
.. x = 2.75 +78/8 = 12.50

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ApusApus ApusApus · Answer 2 · 2019-01-06T12:54:16+01:00

Answer:

Rita made a sign error.

Step-by-step explanation:

Let x be the selling price of each necklace.

We are told that the materials to make each necklace cost $2.75.

Since profit is the difference between selling price and cost.

[tex]\text{Profit}=\text{Selling price- Cost}[/tex]

So profit of Rita from selling one necklace will be:

[tex]\text{Profit of Rita from 1 necklace}=x-2.75[/tex]

To find the profit of Rita from selling 8 necklace we will multiply 8 by profit of 1 necklace.

[tex]\text{Profit of Rita from 8 necklaces}=8(x-2.75)[/tex]

As Rita wants to make a total profit of $78 from selling 8 necklaces, so we will substitute 78 as profit of 8 necklaces.

[tex]78=8(x-2.75)[/tex]

Upon comparing our equation with the given equation we can see that Rita made a sign error as she added the cost with the selling price instead of subtracting the cost from selling price.

Let us find the selling price.

[tex]78=8x-22[/tex]

[tex]78+22=8x[/tex]

[tex]100=8x[/tex]

[tex]\frac{100}{8}=x[/tex]

[tex]12.5=x[/tex]

We can see that the selling price of each necklace will be 12.5, therefore, Rita made a sign error.