Narek and his family are driving home from vacation and plan on taking their time. They drive the same amount of
miles every day. After 4 days of driving, they are 400
miles from home. After 8 days of driving, they are 250
miles from home. Let x represent the number of days
Narek and his family are driving home from vacation and
y represent how far away from home (in miles) they are.

The answer is below

Step-by-step explanation:

Let x represent the number of days  Narek and his family are driving home from vacation and  y represent how far away from home (in miles) they are.

Narek and his family vacation can be represented by coordinate points (x, y) as (4, 400) and (8, 250). We can get an equation using this formula:

The x intercept is the value of x when y = 0:

0 = -37.5(x) + 550

37.5x = 550

x=14.7

The y intercept is the value of y when x = 0:

y = -37.5(0) + 550

y = 550

Therefore the x intercept is 14.7. Which means that when Narek and his family drive for 14.7 days, they are 0 miles from home.

Therefore the y intercept is zero. Which means that when Narek and his family drive for 0 days, they are 550 miles from home.

Comparing the above equation with the equation of a straight line y = mx + b, where m is the slope and b the y intercept, we can get that the slope (m) is -37.5.

The slope is -37.5. This means that for every one day, they have 37.5 miles less to drive to get home.

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!

5+2x=a

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