The original price of a bicycle was $375. now it is on sale for $295. what percentage of the original price was the markdown?

The percentage of the original price that was discounted is 21.33%

Step-by-step explanation:

The original price of a bicycle was $375. Now it is on sale for $295.

The discounted price of a product is calculated as the percentage of discount that you want to apply multiplied by the price of the product. This is the amount of money that is discounted. But to calculate the sale price, the original price of the product must be subtracted minus the discounted quantity.

So, this expressed in this case is:

375-x*375=295

The value of x is the discount that you want to calculate expressed in decimal number. This result will then be multiplied by 100 to obtain the discount expressed as a percentage.

Isolating the value of x you get:

-x*375=295-375

-x*375=-80

x=(-80)÷(-375)

x=0.2133

As a percentage, it is 0.2133*100= 21.33%

The percentage of the original price that was discounted is 21.33%

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.