Some cars turn out to be "lemons" but, the quality of a new car is something that cannot be ascertained until after the car has been driven several hundred miles. the unlucky purchaser of a lemon may then try to unload it, by resale to someone else. let’s assume that 10% of all new cars are lemons, and that 90% of all lemons and 5% of all non-lemons are offered for sale within the first year of ownership. if so, what fraction of all cars offered for sale within the first year are lemons?

Two thirds of the cars offered for sale within the first year are expected to be lemons.

Step-by-step explanation:

The fraction of cars that are offered for sale within the first year and are lemons can be calculated as follow:

The proportion of lemons for sale within the first year is the product of the proportion of lemons within the new cars (10%) and the proportion that are offered for sale, given that they are lemons (90%):

The proportion of no-lemons that are for sale is the product of the proportion of no-lemons within new cars (90%) and the proportion of this group that are offered for sale (5%):

So the fraction becomes

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!

the solution is h=10 because you add 9 to each side of the equation.