SOLUTION: a shop owner orders a number of drinking glasses which she pays R300, while unpacking the glasses, 10 get broken she decide to sell each remaining glasses at R4 more than she pai
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Question 1152383: a shop owner orders a number of drinking glasses which she pays R300, while unpacking the glasses, 10 get broken she decide to sell each remaining glasses at R4 more than she paid for them . she manages to make a profit of R100 on the transaction. how many glasses did she initially order and what was the price the price of each? Answer by ikleyn(52808) (Show Source):
Let x be the value under the question (the original number of glasses).
Then the price for each glass when buying is rupees.
She made R100 profit selling, so she sold for R300 + R100 = R400.
The number of glasses sold is (x-10), according to the condition.
For each of (x-10) glasses sold, she get R4 more than paid per glass buying.
It means that
- = 4. (1)
It is your basic equation.
To solve it, multiply both sides by x*(x-10). You will get
400x - 300*(x-10) = 4x*(x-10).
Simplify step by step and solve
400x - 300x + 3000 = 4x^2 - 40x
4x^2 -40x - 100x - 3000 = 0
4x^2 - 140x - 3000 = 0
x^2 - 35x - 750 = 0
(x-50)*(x+15) = 0
Of the two roots, 50 and -15, only positive value x= 50 is the solution.
ANSWER. 50 glasses were bought at the price of = R6.
CHECK. I will check that the equation (1) is valid.
- = - = 10 - 6 = 4. ! Precisely correct !
