Answer:
The number of beads used must be at least 40 to make a decorated rope of at least 20 feet length. The inequality is:
[tex]6n\geq 240\\n\geq 40[/tex]
Step-by-step explanation:
Let the number of beads used be 'n'.
Now, length of 1 bead = 6 in
∴ Length of 'n' beads = [tex]6\times n=6n\ in[/tex]
Now, minimum length of rope is 20 ft. Converting feet to inches, we get:
[tex]20\ ft =20\times 12=240\ in[/tex]
Now, beads are inserted in the rope. So, the length of rope is same as the length of all the beads joined together.
As per question, length must be at least 20 ft or 240 in.
Therefore, the length of all beads joined together must be at least 240 inches. This gives,
[tex]6n\geq 240\\n\geq \frac{240}{6}\\n\geq 40[/tex]
Therefore, the number of beads used must be at least 40 to make a decorated rope of at least 20 feet length.
