Mathematics, 19.10.2020 05:01 tobydeathstirke

Ainsley walks 3/5 mile in 1/3 of a day. Sarah walks 5/8 mile in 2/6 of a day. Who walked farther, Ainsley or Sarah? Find the unit rate for each girl and then tell who you think walked farther with the correct unit rate given below. *

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Answer from: emilypzamora11

$Ainsley \: walked \: in \: \frac{1}{3} \: \: of \: a \: day \ \: = \frac{3}{5} mile$

$= \frac{1}{3} \times 24 = \frac{3}{5}$

$8 \: hours = \frac{3}{5} \: miles$

$Sarah \: walked \: in \: \frac{2}{6} of \: a \: day \: = \frac{5}{8} miles$

$\frac{2}{6} \times 24 = \frac{5}{8}$

$8 \: hours \: = \frac{5}{8} \: miles$

Let us see who walked more :

$Ainsley \: walked \: = \frac{3 \times 8}{40}$

$= \frac{24}{40} \: miles$

$Sarah \: walked \: = \frac{5 \times 5}{40}$

$= \frac{25}{40} \: miles$

$\frac{24}{40} < \frac{25}{40}$

Sarah walked farther than Ainsley .

$\frac{25}{40} - \frac{24}{40} = \frac{1}{40} \: miles$

∴ Sarah walked farther than Ainsley by 1/40 miles .

Answer from: Quest

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!

Answer from: Quest

add an image !

step-by-step explanation:

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Ainsley walks 3/5 mile in 1/3 of a day. Sarah walks 5/8 mile in 2/6 of a day. Who walked farther, Ai...

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