Based on housing data below which equation can be used to calculate fair housing prices?
Square feet
1900
2000
2200

house price (in the thousands 19)
196
205
225

A. y = 0.087x + 9.286
B. y = 0.097x + 11.142
C. y = 0.074x - 50.48
D. y = 0.087x - 9.286

B. y = 0.097x + 11.142

Step-by-step explanation:

In order to find the best equation to descibe the housing price, we have to calculate the slope of the line  first.

The equation of the line can be written as

where m is the slope and q the y-intercept.

In order to have the most accurate estimate for the slope, we use the first point and the last point, that are:

(1900, 196)

and

(2200, 225)

The slope of the line is calculated as:

So, the slope of the line is 0.097.

Therefore, the correct option is the only one having a slope of 0.097, which is:

B. y = 0.097x + 11.142

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!

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart