The price was lowered by $1,200 which is 40% of $3,000.

Let's call the original length and width of the rectangle  and , respectively.

The initial area, , of the rectangle is equal to the product of the length and the width. We can represent this with the following equation:

Next, let and represent the length and width, respectively, after they have been decreased.  The final area will be equal to , which will be equal to the product of the final length and width.

We are asked to find the change in the area, which essentially means we want to compare and . In order to do this, we will need to find an expression for in terms of  and . We can rewrite and in terms of and .

First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.

= 85% of =

Similarly, if we decrease the width by 20%, we are only left with 80% of the width.

= 80% of =

We can now express the final area in terms of and by substituting the expressions we just found for the final length and width.

= ()() =

Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.

percent change = (100%)

=(100%)

=(100%) = –0.32(100%) = –32%

The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.

The answer is 32.

The original reduction brings the total to  of the original value. Taking a  discount off that price gives  of the original value. This means the reduction had been .

The best way to answer this question is to plug in a number for n. Since you are working with percentages, it may be easiest to use 100 for n.

We know that in the month of February, the cost of this shirt was decreased by 10%. Because 10% of 100 is $10, the new cost of the shirt is $90.

In March, the cost of the shirt decreased another 10%. 10% of 90 is 9, so the cost of the shirt is now $81.

To find the total percentage decrease, you must divide 81 by 100 and subtract it from 1.

1 – (81/100) = 1 – 0.81 = 0.19

The total decrease was 19%.

The easiest way to do percentage changes is to keep them all in one equation. Therefore, we would say that an increase of 15% is the same as multiplying the original value by 1.15. Likewise, we would say that a discount by 35% is the same as multiplying the original by .65.

For our problem, let the hat cost X dollars originally. Therefore, after its increase, it costs 1.15X dollars. Now, we can consider this new price as the whole to which the discount will be applied. Therefore, a 35% reduction is (1.15X) * 0.65.

Simplifying, we get 0.7475, or 74.75%.

For these type of questions, it is always best to pretend that we are beginning with a $100 item and to calculate from there.

If an item that is $100 is discounted by 35%, and then another 10%, the new price is 58.5%.

The price difference (discount) is $41.5 for every $100, or:

The total discount is 41.5%.

Since we are looking for the change, we must take the

(Ending Point – Starting Point)/Starting Point * 100%

(22752 – 12979)/12979 * 100%

9773/12979 * 100%

0.753 * 100%

75%

This is a percentage increase problem. 

Easiest approach :  2500 x 1.12 = 2800

In this way you are adding 12% to the original.

Using the formula, find 12% of 2500

12/100 = x/2500, 

30000 = 100x

300 = x

Now add that to the original to find the new production:

2500 + 300 = 2800

If we plug-in a radius of 5, then a 20% increase would give us a new radius of 6 (which is 1.2 x 5).  The area of the new circle is π(6)2 = 36π, and the area of the original circle was π(5)2 = 25π .  The numerical increase (or difference) is 36π - 25π = 11π.  Next we have to divide this difference by the original area: 11π/25π = .44, which multiplied by 100 gives us a percent increase of 44%.  The percent increase = (the numerical increase between the new and original values)/(original value) x 100. The algebraic solution gives us the same answer.  If radius r of a certain circle is increased by 20%, then the new radius would be (1.2)r.  The area of the new circle would be 1.44 π r2 and the area of the original circle πr2.  The difference between the areas is .44 π r2, which divided by the original area, π r2, would give us a percent increase of .44 x 100 = 44%.

$1,800,800 divided by 100 equals 18,008 and $2,130,346 divided by 18,008 is 118.3

So we know that $2,130,346 is 118.3% of the sales in the previous year. Hence sales increased by 18.3%.