It takes Marty 1 1/4 hours to get ready for school. If 1/5 of that time is used to shower and 1/3 of that time is used to eat breakfast, how long does it take to shower and eat breakfast

  2/3 hour

Step-by-step explanation:

We can add the fractions, then multiply by the time, or we can multiply each by the time and add the results.

  (1/5 +1/3)(1 1/4) = (8/15)(5/4) = (4·2·5)/(3·5·4) = 2/3 . . . hours

alternatively, ...

  (1/5)(1 1/4) +(1/3)(1 1/4) = (1/5)(5/4) +(1/3)(5/4)

     = 1/4 +5/12 = 3/12 +5/12 = 8/12 = 2/3 . . . hours

It takes Marty 2/3 hours (40 minutes) to shower and eat breakfast.

the total amount of time

it takes to shower and eat breakfast is 2/3 hour.

Step-by-step explanation:

The total amount of time that it takes Marty to get ready for school is 1 1/4 hours. Converting to improper fraction, it becomes 5/4 hours.

If 1/5 of that time is used to shower, it means that the it takes to shower is 1/5 × 5/4 = 1/4 hour.

If 1/3 of that time is used to eat breakfast, it means that the time it took to eat breakfast is 1/4 × 5/4 = 5/12 hour.

Therefore, the total amount of time

it takes to shower and eat breakfast is

1/4 + 5/12 = 8/12 = 2/3 hour

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

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!

2.83941151 would be the answer you're looking for! : )