I have worked for days on this and went to every website and test I could find but cannot wrap my brain around this.

Word problems give me great difficulty and I am supposed to construct a quadratic equation for this. I'd really appreciate some help.

if a retailer spends $48 to purchase some items and two of them were broken in the store and the remaining mugs were sold for $3 above the cost of the mugs, profit was $22

I have to construct an equation to solve for the number of mugs that were originally purchased.

I think the formula is supposed to be ax (sq) +bx+c=0 but I have no idea how to plug in the numbers or if this is a proper formula. I have worked for days and even looked at wikipedia and can't get it. Please help :confused:

Profit = Revenue - Cost.

The Profit is $22. The cost is $48.

Now, the trickiest part. After 2 are broken, the mugs sell for $3 more, a piece, then what they paid for them.

Each mug cost 48/n dollars. There are n-2 of them top sell.

\overbrace{22}^{\text{profit}}=\underbrace{(\frac{ 48}{n}+3)(n-2)}_{\text{revenue}}-\overbrace{48}^{\text{cost}}

The quadratic is 3n^{2}-28n-96=0

Solve away. One solution will be negative, therefore, erroneous.

Factor, use the quadratic formula, complete the square. Whatever.