ESTIMATING PERCENTS

Percentage can be estimated as follows. 

Comparing the given number to 100

or

Ratio between the given number and 100

or

 Saying per 100

For example, 

30 %  =  30/100  or  30 : 100

Formula

Let us say that the original value x is changed to the other value y.

To estimate the above change in percent, we have to divide the absolute difference of x and y (amount of change) by the original value.

That is, the formula to estimate the percent is 

=  (|x - y| / x) ⋅ 100%

Apart from the above stuff, if you wish to learn more about percents, 

Please click here

Example 1 :

The price of a camera is $250. The price is increased to $262.50. Estimate what percent of the price is increased. 

Solution : 

Difference between the old price and new price is 

=  262.50 - 250

=  $12.50

Percent of change is 

=  (Difference in price / Old price) ⋅ 100%

=  (12.50 / 250) ⋅ 100%

=  5%

So, 5% of the price of the camera is increased. 

Example 2 :

An item is originally priced $80. A discount is given and the item is bought for $68. Estimate what percent of discount received.  

Solution : 

To find the actual discount received, find the difference between the original price and the price after the discount.    

Discount  =  80 - 68

Discount  =  $12

Percent of discount is 

=  (Discount / Original price) ⋅ 100%

=  (12 / 80) ⋅ 100%

=  15%

So, the percent of discount received is 15%. 

Example 3 :

A grocery store has two recycling machines outside. The first recycle machine took in 240 plastic bottles and 180 metal cans. The second took in 30 percent more plastic bottles but 10 percent less metal cans. The second machine recycled what percent more items than the first (rounded to the nearest percent)?    

Solution : 

First recycle machine : 

No. of plastic bottles  =  240

No. of metal cans  =  180

Total number of items  =  240 + 180  =  420

First recycle machine : 

No. of plastic bottles  =  1.3 ⋅ 240  =  312

No. of metal cans  =  0.9 ⋅ 180  =  162

Total number of items  =  312 + 162  =  474

Difference between the total number of items recycled by the first machine and the second machine is 

=  474 - 420

=  54

The second machine recycled 54 more items than the first machine.

Percent increase from the first machine to second : 

=  (54 / 420) ⋅ 100%

≈  13%

So, the second machine recycled about 13% more items than the first machine.

Example 4 :

Michael and Richard are partners in a business and share the profit in the ratio 2 : 3. Richard gets what percent more profit than Michael ?   

Solution : 

Add the two terms in the ratio and take the result as total parts.

Then, the total parts is

=  2 + 3

=  5

Out of the total parts 5, share of Michael is 2 parts and Richard is 3 parts. 

Richard gets 1 part of profit more than Michael. 

Percent increase from Michael's share to Richard's share : 

=  (1 / 2) ⋅ 100%

=  50%

So, Richard gets 50% more profit than Michael. 

Example 5 : 

The kinetic energy of an object is given by (mv² / 2) where m is the mass and v is its velocity. A radio active element loses 15 percent of its mass and 20 percent of its velocity. By what percent has its kinetic energy decreased ?     

Solution : 

The kinetic energy of the object is

=  mv² / 2

=  0.5mv²

After 15 percent decrease in mass and 20 percent decrease in velocity, the kinetic energy is

=  (0.85m)(0.8v)² / 2

=  (0.85m)(0.64v²) / 2

=  0.544v² / 2

=  0.272mv²

Difference :

=  0.5mv² - 0.272mv²

=  0.228mv²

Percent  decrease : 

=  (0.228mv² / 0.5mv²)  ⋅ 100%

=  45.6%

So, 45.6 percent of kinetic energy has decreased. 

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