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!
