Question

If the center thickness of a Tootsie Roll Pop varies more than 0.2 cm from the target thickness of 7.5 cm, the pop must be thrown out. Write and solve an absolute value equation to find the extreme acceptable size for the center thickness of a Tootsie Roll Pop.

Sorry about these weird questions....I need to answer each fully correct or I won’t pass Alg 2

Answer 1

If the allowable centre thickness = x

- The absolute value equation representing the condition for an acceptable centre thickness of a Tootsie Roll Pop described is

|x - 7.5| ≤ 0.2

- To solve for the extreme acceptable size for the centre thickness of a Tootsie Roll Pop, the absolute value equation becomes

|x - 7.5| = 0.2

- The extreme acceptable size for the centre thickness of a Tootsie Roll Pop is

A lower limit of 7.3 cm

An upper limit of 7.7 cm

Explanation:

Target thickness of a Tootsie Roll pop= 7.5 cm

And the centre thickness of the tootsie roll pop should not vary more than 0.2 cm from the target thickness.

Let the allowable centre thickness be x, the absolute value equation representing the condition described is then

|x - 7.5| ≤ 0.2

To solve for the extreme acceptable size for the centre thickness of a Tootsie Roll Pop, the absolute value equation becomes

|x - 7.5| = 0.2

To solve this, the two solutions include

(x - 7.5) = 0.2 and -(x - 7.5) = 0.2

Taking the two, one at a time,

(x - 7.5) = 0.2

x = 7.5 + 0.2 = 7.7 cm

And

-(x - 7.5) = 0.2

x - 7.5 = -0.2

x = 7.5 - 0.2 = 7.3 cm

Hence, the extreme acceptable size for the centre thickness of a Tootsie Roll Pop is

A lower limit of 7.3 cm

An upper limit of 7.7 cm

Hope this Helps!!!