Question 194097: a retailer spent $48.00 to purchase a number of special mugs. 2 broken in store, but by selling each of remaining mugs for $3.00 above original cost per mug, made $22.00 profit.
a. if the price for n mugs is $48, how can i express the cost per mug?
b. using answer in step a, how do i express selling price per mug?
c. since two broken how do i express # of mugs available for sale?
d. using b and c construct expression for amount of 4 made on sale of remaining
e. how do i express relationship between money made, the cost and the profit
what i come up so far.......still confused as exactly how to express each listed above...thanks
Let n = the number of mugs purchased by the retailer
Let n-2 = the number of mugs available for sale (the retailer broke two)
Let (48/n) - the cost of each mug purchased by the retailer ($48 spent divided by the number of mugs)
If she sold each mug for a 3 profit
(3+(48/n)) is the sale price of each mug
(n-2)(3+(48/n)) = the total sales (the number of mugs sold*the price)
the total sales = cost + $22 profit
(n-2)(3+(48/n))=48+$22
If (n-2)(48/n+3) - 48 = 22 then expanding brackets:-
48 - 96/n + 3n - 6 - 48 = 22 and rearranging
3n - 96/n - 28 = 0 and multiplying through by n gives
3n^2 - 28n - 96 = 0 which is the standard form of a Q.E.
Factorising to (3n + 8)(n - 12) = 0 therefore:-
n = - 8/3 or 12
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a retailer spent $48.00 to purchase a number of special mugs. 2 broken in store, but by selling each of remaining mugs for $3.00 above original cost per mug, made $22.00 profit.
a. if the price for n mugs is $48, how can i express the cost per mug?
Ans: 48/n
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b. using answer in step a, how do i express selling price per mug?
Ans: (48/n)+3 dollars
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c. since two broken how do i express # of mugs available for sale?
Ans: n-2
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d. using b and c construct expression for amount of 4 made on sale of remaining
Ans: ? What do you mean by "amount of 4" ?
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e. how do i express relationship between money made, the cost and the profit
what i come up so far.......still confused as exactly how to express each listed above...thanks
Let n = the number of mugs purchased by the retailer
Let n-2 = the number of mugs available for sale (the retailer broke two)
Let (48/n) - the cost of each mug purchased by the retailer ($48 spent divided by the number of mugs)
If she sold each mug for a 3 profit
(3+(48/n)) is the sale price of each mug
(n-2)(3+(48/n)) = the total sales (the number of mugs sold*the price)
the total sales = cost + $22 profit
(n-2)(3+(48/n))=48+$22
If (n-2)(48/n+3) - 48 = 22 then expanding brackets:-
48 - 96/n + 3n - 6 - 48 = 22 and rearranging
3n - 96/n - 28 = 0 and multiplying through by n gives
3n^2 - 28n - 96 = 0 which is the standard form of a Q.E.
Factorising to (3n + 8)(n - 12) = 0 therefore:-
n = - 8/3 or 12
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That all looks good to me.
Accept the solution, n = 12.
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Cheers,
Stan H.
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