<u>ANSWER: </u>
The algebraic expression for number of ribbons is
and the algebraic expression for length of ribbon is ![\frac{25 x}{3} \text { feet }](https://tex.z-dn.net/?f=%5Cfrac%7B25%20x%7D%7B3%7D%20%5Ctext%20%7B%20feet%20%7D)
<u>SOLUTION:
</u>
Given, 20 feet of ribbon, cutting ribbon into
inches or
inch lengths to make bracelets.
Let us convert the mixed fraction to improper fractions.
![7 \frac{1}{2}=\frac{7 \times 2+1}{2}=\frac{15}{2} \text { and } 6 \frac{3}{4}=\frac{6 \times 4+3}{4}=\frac{27}{4}](https://tex.z-dn.net/?f=7%20%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B7%20%5Ctimes%202%2B1%7D%7B2%7D%3D%5Cfrac%7B15%7D%7B2%7D%20%5Ctext%20%7B%20and%20%7D%206%20%5Cfrac%7B3%7D%7B4%7D%3D%5Cfrac%7B6%20%5Ctimes%204%2B3%7D%7B4%7D%3D%5Cfrac%7B27%7D%7B4%7D)
Let, the length of bracelets can be made be “x”
First we have to remove the excess length of ribbon and then we have to divide the remaining with length of bracelet we want.
![\text { number of ribbons }=\frac{\text { length of ribbon-excess ribbon.}}{\text {length of bracelet}}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20number%20of%20ribbons%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20length%20of%20ribbon-excess%20ribbon.%7D%7D%7B%5Ctext%20%7Blength%20of%20bracelet%7D%7D)
]
So, the algebraic expression for number of ribbons is ![\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B20%20%5Ctext%20%7B%20feet%20%7D-%5Cleft%5C%7B%5Cfrac%7B20%20%5Ctext%20%7B%20feet%20%7D%7D%7Bx%7D%5Cright%5C%7D%7D%7Bx%7D)
Now, let us find the algebraic expression for feet of ribbon to make 100 ribbons.
We have 100 bracelets of length x, then total length = 100 × x
length of ribbon = 100x inches
![\begin{array}{l}{=100 \mathrm{x} \times \frac{1}{12} \text { feet }} \\\\ {=\frac{25 x}{3} \text { feet }}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%3D100%20%5Cmathrm%7Bx%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B12%7D%20%5Ctext%20%7B%20feet%20%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B25%20x%7D%7B3%7D%20%5Ctext%20%7B%20feet%20%7D%7D%5Cend%7Barray%7D)
So, the algebraic expression for length of ribbon is ![\frac{25 x}{3} \text { feet }](https://tex.z-dn.net/?f=%5Cfrac%7B25%20x%7D%7B3%7D%20%5Ctext%20%7B%20feet%20%7D)
Hence, the algebraic expression for number of ribbons is
and the algebraic expression for length of ribbon is ![\frac{25 x}{3} \text { feet }](https://tex.z-dn.net/?f=%5Cfrac%7B25%20x%7D%7B3%7D%20%5Ctext%20%7B%20feet%20%7D)