SOLUTION: LAST season,a pair of jeans cost $35.00, this season the pair of jeans increased by 25%, Later in the season the jeans were put on sale for 25% off. How much did the jeans cost at

Question 1045320: LAST season,a pair of jeans cost $35.00, this season the pair of jeans increased by 25%, Later in the season the jeans were put on sale for 25% off. How much did the jeans cost at the beginning of the season? And what was their sale price? Where you surprised by the sale price of the jeans? Why or why not? What would the jeans cost if they had gone on sale by 25% first, and then had their price increased by 25%? Why?
Found 2 solutions by jorel555, KMST:
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
Last season, the jeans were $35. This season, they are 35+.25(35), or 1.25(35), which equals $43.75.
When they are put on sale, they are (1-.25)43.75, which equals $32.8125 as their sale price.
If the jeans had gone on sale first, then increased, they would be (1-.25)(1+.25)x35=$32.8125.
The resultant price is the same because the process getting to the price is the same, only reversed: (1+.25)(1-.25)x=(1-.25)(1+.25)x. ☺☺☺☺
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Percentages are ratios, and sometimes we can write them as decimals: .
At the beginning of this season the price of the jeans had increased from by
.
So, at the beginning of this season the price of the jeans was
.
When, later in the season. the jeans were put on sale for 25% off, the discount was ,
so the new, sale price was calculated as
,
which should have been rounded to .

We should not be surprised to see that 25% of a lower starting price
is less than 25% of a higher price.
When the price is first increased by 25%, the increase is of just ,
but when they apply the 25% discount to the larger jacked up price, the discount is of a larger amount.
Of course, the final price will be lower than the fist price.

Of course, if the starting price had been cut by 25% first, to get a smaller second price,
adding 25% of that smaller price later would have been adding a lesser mark up, and the final price would have been less.
Why? Because the initial discount and the final price increase were calculated as the same percentage base on different prices,
and when you apply the discount first,
you get a smaller price that is used to calculate a smaller price increase.
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