The length of a backpack of capacity 30 liters is 53 cm.

Calculate the length of a mathematically similar backpack of capacity 20 liters.

Can someone explain to me this problem and how to solve it?

The length for 20 litre capacity will be 35.334 cm

Step-by-step explanation:

Given:

30 capacity litre corresponds to 53 cm

To Find :

20 liters.

Solution:

This representation is of double number line

i.e one line represents the capacity in litre and other length.

Now  at 30 litre corresponds to 53 cm

So the ratio , 1 litre representation,

1:30/53

i.e. 53/30=1.7667

This ratio will be constant through out the line.

So for 20 litre it will be ,as

=20*(1.7667)

=35.334 cm

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!

hi,

6x times 4 is 24x and 5 times 4 is 20, so the answer is 24x+20.

hope this and for a little humor i am groot.