Chapter 14, Problem 1MPS

To determine

To Find: The number of necklaces sold.

Answer to Problem 1MPS

The number of necklaces sold is $60$ .

Explanation of Solution

Given:

The cost of the necklaces is $6250.

The cost of 40 necklaces is $7130.

The purchase price is three less than the selling price.

Calculation:

Consider the number of necklaces purchased is $x$ and cost of each of the necklace is $y$ .

Then, from the given information,

  $\begin{array}{l}xy=\$6250\\ y=\frac{\$6250}{x}\end{array}$

From the given data,

  $\begin{array}{l}\left(x-40\right)\left(y+3\right)=\$7130\\ xy-3x-40y=7250\\ x\left(\frac{6250}{x}\right)-3x-40\left(\frac{6250}{x}\right)=7250\\ 6250-3x-\frac{250000}{x}=7250\end{array}$

Solve further as,

  $\begin{array}{l}6250-3x-\frac{250000}{x}=7250\\ -3x-\frac{250000}{x}=1000\\ -3x^2-25000=1000x\\ -3x^2-1000x-25000=0\end{array}$

Then, the solution of the above equation is,

  $\begin{array}{c}x=\frac{-\left(1000\right)\pm \sqrt{{1000}^2-4\left(-3\right)\left(250000\right)}}{2\left(-3\right)}\\ =\frac{-1000\pm 2000}{-12}\\ =-166.66,500\end{array}$

As then number of necklaces is not negative than the correct answer is $500$ .

The number of necklaces sold is $500-40=460$ .