(adsbygoogle = window.adsbygoogle || []).push({}); 1. A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the orignial cost per mug, she made a total profit of $22. Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.How many mugs were purchased? What was the original cost per mug? What profit was made on each mug?

So first - my original cost per mug equation: C=48/n

Selling price of mug: S=(48/n)+3

number of mugs sold: n-2

number of mugs bought: n

my attempt at solving: (n-2) * ((48/n)+3) = 48 +22

my thought process here was i took the number of mugs able to be sold (n-2) multiplied by the selling price of each mug = ((48/n)+3) to get the total money made 48+22. Where 22 is the profit she made, and 48 was the original purchase price.

so first thing i did was get rid of the N in the denominator of selling price. multiplying (n-2) times n, and ((48/n)+3) times n = and then 70 times n

simplifying gets me (n^2-2n) * (48 +3n) = 70

multiplying with distributive property :

3n^3+42n^2-96n = 70 n

isolate 0 gets me

3n^3 +42n^2 -166n=0

factor out one n:

n(3n^2+42n-166)=0

now im trying to factor my quadratic equation. But i just cant. nothing works.

Ive long since figured N to be 12, simply by trial an error. But i need to show equations. And i have no idea where my math went in error. Can anyone show me an equation to use, or where i went wrong or help me to get the proper answer. Thank you in advance

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# Homework Help: Algebraic problem: forming equation?

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