When the automobile manufacturer releases a new model in its WOW series, it promises that drivers can expect to get mileage that varies by no more than 6.5 miles per gallon from its field-tested average of 28.4 miles per gallon. Which solution represents the range of mileage you can expect from this car?

Question

rsadhvika · Answer

I know the answer is $28.4 \pm 6.5$

rsadhvika · Answer

But I am stuck at solving this problem by using an absolute value equation... can we turn the given info to an absolute equaiton and sovle ?

rsadhvika · Answer

like $28.4  = |x| + ... $ something

rsadhvika · Answer

I feel somehow i forgot the basics :(

whpalmer4 · Answer

|28.4-mileage| <= 6.5

test it out: if the mileage achieved is the lower bound (28.4-6.5 = 21.9),
|28.4-21.9| = | 6.5| = 6.5 <= 6.5
if the mileage achieved is the upper bound (28.4+6.5 = 34.9),
|28.4-34.9| =  | -6.5| = 6.5 <= 6.5

whpalmer4 · Answer

You know that the magnitude of the predicted mileage - actual mileage is the variation, right?  So our equation is the same as saying 

28.4-6.5 <= mileage <= 28.4+6.5

and you should be able to convince yourself that the two forms are equivalent...

rsadhvika · Answer

thanks a lot ! i get it completely now xD