Question
Kenzie finished recording the last song for her new album . The song was 4 minutes and 47 seconds long. The song must be with in 30 seconds of 250 seconds long to fit in the recording space left on the album.
Write an absolute value inequality to represent the situation and solve. Will the last song fut on the album ?
Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
We will construct an inequality which models the situation with the help of the concept of absolute value.
The correct answer is: Combining the above the two equations, we get 220 ≤ x ≤ 280
Step by step solution:
Given,
Let Length of the last song (in seconds)be x
Space left on the album for the last song = 250 sec
Error that is allowed in length of the song = 30 sec
We form an equation in terms of the length of the song (in sec).
And
We can rewrite the above equations as
And
We combine the above two cases to get the following equation.
Thus, the equation representing the given situation is
Now, we solve this equation.
Using the definition of absolute value,
We get two possibilities,
,
Simplifying, we get
Subtracting 250 both sides, we have
Multiplying by -1 throughout, we get
For 
,
Adding 250 both sides, we get
Thus, we get
Combining the above the two equations, we get
Length of the last song is given as 4 min 47 sec
As 1 min = 60 sec, we have
Length of the last song (in sec)= 4×60+47 = 240+47 = 287
But the range of x gives that the length of the song can be maximum 280 sec.
Thus, the last song will not fit the album.
And
We can rewrite the above equations as
And
We combine the above two cases to get the following equation.
Thus, the equation representing the given situation is
Now, we solve this equation.
Using the definition of absolute value,
We get two possibilities,
,Simplifying, we get
Subtracting 250 both sides, we have
Multiplying by -1 throughout, we get
,Adding 250 both sides, we get
Thus, we get
Combining the above the two equations, we get
Length of the last song is given as 4 min 47 sec
As 1 min = 60 sec, we have
Length of the last song (in sec)= 4×60+47 = 240+47 = 287
But the range of x gives that the length of the song can be maximum 280 sec.
Thus, the last song will not fit the album.
Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.
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A. The cost of 4 tetras is the same as the cost of a rainbow fish.
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For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).
