Question

To allow for a models height,a designer is willing to use models that require him to change hems either up or down 2 inches.the length of the skirts is 20 inche
a.write an absolute value equation that represents the length of the skirts.

b.what is the range of the lengths of the skirts?

c.if a 20-inch skirt was fitted for a model that is 5 feet 9 inches tall,will the designer use 6-foot-tall model?

Answer 1

(a)

Let's assume

the range of the lengths of the skirts is t inch

now, we are given

to change hems either up or down 2 inches

so, total change in length should be 2

so, we will have right side =2

the length of the skirts is 20 inch

this will be either greater or lesser to length of skirts

so, the difference between them will be t-20

so, we get

$|t-20|=2$

(b)

now, we can find range

firstly, we will break  absolute sign

$|t-20|=-(t-20)$ for t<20

$|t-20|=(t-20)$ for t>20

because value of |t-20| must be positive

so, we get

$-(t-20)=2$

Multiply both sides by -1

$-(t-20)\times -1=2\times -1$

$(t-20)=-2$

Add both sides by 20

$(t-20)+20=-2+20$

$t=18$

$(t-20)=2$

Add both sides by 20

$(t-20)+20=2+20$

$t=22$

so, the range of the lengths of skirts is

18 in to 22 in..........Answer

(c)

Firstly, we will find difference in height of the model

5 feet 9 inches $=12\times 5+9=69in$

6 feet =$12\times 6=72in$

now, we can find difference in height

$=72-69=3in$

and we are given

difference in length of skirts =2 in

so, the difference in height is greater than the difference in length of skirts

so, the answer is NO