Question 1206365: A car dealership is having a contest to win a new truck. In order to win a chance at the truck, you must first guess the number of keys in the jar within 5 of the actual number. The people who are within this range then get to try a key in the ignition of the truck. Suppose there are 697 keys in the jar. Write an absolute value equation that will reveal the highest and lowest guesses in order to win a chance at the truck. What are the highest and lowest guesses that will qualify for a chance to win?
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! abs(x-697) <= 5 is the equation you want.
this equation can be split into two parts.
when (x-697) is positive, it becomes (x-697) <= 5.
when (x-697) is negative, it becomes -(x-697) <= 5
that's because, by definition, abs(x) = x when x is positive and equals -x when x is negative.
x represents the expression within the absolute value sign.
x by itself is an expression within the absolute value sign.
x - 697 is an expression within the absolute value sign.
absolute value of an expression can be written as abs(x) or it can be written as |x|, where the vertical lines indicated that the absolute value expression is between them.
you start with abs(x-697) <= 5
when (x-697) is positive, the equation becomes (x-697) <= 5
when (x-697) is negative, the equation becomes -(x-697) <= 5
if you multiply both sides of this inequality by -1, the inequality reverses and you are left with (x-697) >= -5.
to solve, start with (x-697) <= 5
add 697 to both sides of that inequality to get x <= 697 + 5 which simplifies to x <= 702.
next start with -(x-697) <= 5.
multiply both sides of that inequality by -2 to get (x-697) >= -5.
add 697 to both sides of that inequality to get x >= 697 - 5 which simplifies to x >= 692.
abs(x - 697) <= 5 means 692 <= x <= 702.
the highest guess would be 702 and the lowest guess would be 692.
those guesses and any guess in between provides a chance to win the truck.
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
Again, the question should go about an inequality - - - not about equation.
There is some stone in the mind of the "math composer", which prevents him (or her) to call the things by their real/proper names.
This stone is the absence of adequate mathematical education,
which is needed to create true Math problems.
Answer by greenestamps(13200)  (Show Source):
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