20 feet of ribbon, cutting ribbon into 7 1/2 inches or 6 3/4 inch lengths to make bracelets. Write an algebraic expression that can be use to figure out how many bracelets can be made.How can you change above expression is you want to figure out how many feet of ribbon needed to make 100 bracelets.

ANSWER:  The algebraic expression for number of ribbons is [tex]\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}[/tex] and the algebraic expression for length of ribbon is [tex]\frac{25 x}{3} \text { feet }[/tex]SOLUTION: Given, 20 feet of ribbon, cutting ribbon into [tex]7\frac{1}{2}[/tex] inches or [tex]6\frac{3}{4}[/tex] inch lengths to make bracelets. Let us convert the mixed fraction to improper fractions.[tex]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}[/tex]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. [tex]\text { number of ribbons }=\frac{\text { length of ribbon-excess ribbon.}}{\text {length of bracelet}}[/tex][tex]\left.=\frac{20 \text { feet }-\left\{\frac{20 \text { feep }}{x}\right.}{x} \text { [we know that, }\{x\} \text { is fractional part of } x\right[/tex] ]So, the algebraic expression for number of ribbons is  [tex]\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}[/tex]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[tex]\begin{array}{l}{=100 \mathrm{x} \times \frac{1}{12} \text { feet }} \\\\ {=\frac{25 x}{3} \text { feet }}\end{array}[/tex]So, the algebraic expression for length of ribbon is [tex]\frac{25 x}{3} \text { feet }[/tex]Hence, the algebraic expression for number of ribbons is  [tex]\frac{20 \text { feet }-\left\{\frac{20 \text { feet }}{x}\right\}}{x}[/tex] and the algebraic expression for length of ribbon is [tex]\frac{25 x}{3} \text { feet }[/tex]