There are three consecutive even numbers such that twice the first is 20 more than the second. find the number

Step-by-step explanation:

2n is an even number.

Your three even numbers are 2n, 2n + 2, 2n + 4

Twice the first is 20 more than the second.

2n * 2 = 2n + 2 + 20

Simplify:

4n = 2n + 22

Use simultaneous equations to solve n.

4n = 2n + 22 - 2n

2n = 22 ÷ 2

n = 11

Subsitiye n into the three even numbers.

2n, 2n + 2, 2n + 4

2 * 11, 2 * 11 + 2, 2 * 11 + 4

22, 24, 26

Check that the numbers meet the requirements.

22 * 2 = 24 +20

44 = 44

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!

answer: 59

step-by-step explanation: