Mr Badger buy 12 pens for $x each. The price of the pens have now increased by 15
cents each. And he can only afford to buy 10 pens at the same total cost as before.
What was the original price of each pen?
cost of each at original price --- x
new price = x+15/100
10(x + 15/100) = 12x
10x + 3/2 = 12x
2x = 3/2
x = 3/4
original cost of pen was $.75 or 75 cents
check:
new cost = 90 cents
Is 10(90) = 12(75) ? YES
Let's assume the original price of each pen was $y.
Originally, Mr. Badger bought 12 pens, so the total cost would be 12y dollars.
The price of each pen has now increased by 15 cents, or 0.15 dollars. Therefore, the new price of each pen is y + 0.15 dollars.
Mr. Badger can now only afford to buy 10 pens at the same total cost as before, which was 12y dollars.
So, we can set up the equation:
10(y + 0.15) = 12y
Simplifying the equation:
10y + 1.5 = 12y
Rearranging the equation:
1.5 = 12y - 10y
1.5 = 2y
Dividing both sides by 2:
y = 0.75
Therefore, the original price of each pen was $0.75.
To find the original price of each pen, we need to set up an equation based on the given information.
Let's assume the original price of each pen is "y" dollars.
According to the problem, Mr. Badger initially bought 12 pens at a price of "x" dollars each. So, the total cost of 12 pens can be calculated as 12x dollars.
The price of each pen has now increased by 15 cents. Since there are 100 cents in a dollar, the price increase in dollars will be 15/100 * 12 = 3/20 * 12 = 36/20 = 1.8 dollars.
As Mr. Badger can only afford to buy 10 pens at the same total cost as before, the cost of 10 pens should be equal to the original cost of 12 pens. Therefore, we have the equation:
10(y + 1.8) = 12x
Simplifying the equation:
10y + 18 = 12x
10y = 12x - 18
Now that we have an equation with two variables (y and x), we need additional information to solve it.