Answer:
The cost price of the article was Nu 1,000
The original selling price was Nu 1,120
The second selling price was Nu 1,200
Step-by-step explanation:
System of Equations
Let's call:
x = Original selling price of the article
y = Cost of the article
The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:
0.12y = Original profit
Setting up the equation, we have:
[tex]x-y=0.12y[/tex]
The second condition states the selling price is 80 Nu more than before, that is:
x+80= Second selling price of the article
y = Cost of the article (it doesn't change)
The profit of this condition is 20%, thus:
0.2y = Second profit
This produces a second equation:
[tex]x+80-y=0.2y[/tex]
Let's put both equations together to form a system of equations:
[tex]x-y=0.12y[/tex]
[tex]x+80-y=0.2y[/tex]
Operating on both equations:
[tex]x=1.12y[/tex]
[tex]x=1.2y-80[/tex]
Equating both equations, we have an equation with only y's:
[tex]1.12y=1.2y-80[/tex]
Subtracting 1.2y on each side:
[tex]1.12y-1.2y=-80[/tex]
Operating:
[tex]-0.08y=-80[/tex]
Solving:
[tex]\displaystyle y=\frac{-80}{-0.08}=1,000[/tex]
a)
The cost price of the article was Nu 1,000
b) The selling price of the article will be calculated in both cases:
Original selling price: x=1.12y= 1.12*1000=1,120
The original selling price was Nu 1,120
The second selling price was x+80=1,200
The second selling price was Nu 1,200
