A number is doubled, then decreased by 13.7. The result is greater than 125.28. What is the smallest integer that satisfies this condition?

x > 69.49

Step-by-step explanation:

Step 1: Write out equation

2x - 13.7 > 125.28

Step 2: Add 13.7 to both sides

2x > 138.98

Step 3: Isolate x by dividing both sides by 2

x > 69.49

So x has to be greater than 70 in order to fit into the question context.

70

Step-by-step explanation:

Let x be the desired integer. Then 2x-13.7>125.28. Adding 13.7 to both sides gives 2x>138.98, and dividing both sides by 2 gives x>69.49. The smallest integer that is greater than 69.49 is .

Hope this helped! :)

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

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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

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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

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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!