Question 1163463: A market woman purchased a number of plates for GH¢ 150.00. Four the plates got broken while transporting them to her shop. By selling the remaining plates at a profit of GH¢ 1.00 on each, she made a total profit of GH¢ 6.00. How many plates did she purchase?
Note: where GH¢ stands for Ghana Cedis
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
A market woman purchased a number of plates for GH¢ 150.00. Four the plates got broken while transporting them to her shop.
By selling the remaining plates at a profit of GH¢ 1.00 on each, she made a total profit of GH¢ 6.00. How many plates did she purchase?
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Let n be the number of plates she purchased.
Then the price she paid for each plate while purchased is  money units.
She then sold (n-4) plates for 150+6 = 156 money units, so her price while selling was  .
The difference of prices was 1 money unit, according to the condition.
It gives you an equation
- = 1.
It is your base equation.
To solve it, multiply both sides by n*(n-4). You will get then
156n - 150*(n-4) = n*(n-4).
Simplifying, you get
n^2 - 10n - 600 = 0.
Factor left side
(n-30)*(n+20) = 0.
Of two roots, 30 and -20, only positive value n= 30 is the solution to the problem.
ANSWER. 30 plates.
CHECK.  -  =  - = 6 - 5 = 1 money unit. ! Correct !
Solved.
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