Question

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?

Answer 1

Rita made a sign error.

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.

`\text{Profit}=\text{Selling price- Cost}`

So profit of Rita from selling one necklace will be:

`\text{Profit of Rita from 1 necklace}=x-2.75`

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

`\text{Profit of Rita from 8 necklaces}=8(x-2.75)`

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

`78=8(x-2.75)`

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.

`78=8x-22`

`78+22=8x`

`100=8x`

`(100)/(8)=x`

`12.5=x`

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

Answer 2

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