Answered

Get the best answers to your questions with the help of IDNLearn.com's experts. Get comprehensive and trustworthy answers to all your questions from our knowledgeable community members.

Giovanni has been hired by a local clothing accessory store to make decorative belts that have green and blue beads carefully glued on them. these belts are meant for a waist size of around 28inches. each bead (green or blue) is about 1 cm wide, and Giovanni has been told to put anywhere between 70 and 74 total beats on each belt (this makes a belt with 70 to 74 cm of Beads which is 27.5 to 29.1 inches.) the store once these beads to consist of mostly green beads but also wants to have a noticeable amount of blue beads, in fact, the store has specified that the ratio of green beads to Blue beads must be at least 1: 4 and at most 1: 6

Write a system of inequalities to model this scenario.

Sagot :

The system of inequalities that model the number and types green (g)

and blue (b) beads in a belt are as follows;

  • 70 < g + b < 74
  • 10 < g < 14
  • 56 < b < 63
  • [tex]\underline{\dfrac{1}{4} \leq \dfrac{b}{g} \leq \dfrac{1}{6}}[/tex]

How can s system of inequalities be written?

The waist size for the belt = ±28 inches

The x represent the number of beads on each belt, we have;

Number of beads per belt 70 < x < 74

Minimum ratio of blue to green beads = 1 : 4

Maximum ratio of blue to green beads = 1 : 6

Therefore;

Minimum number of blue beads = [tex]\frac{70}{1 + 6}[/tex] = 10

Maximum number of blue beads = [tex]\frac{74}{1 + 4}[/tex] ≈ 14

The number of blue beads, b, in a belt is therefore;

  • 10 < g < 14

Minimum number of green beads = [tex]\frac{4}{1 + 4}[/tex] × 70 = 56

Maximum number of green beads = [tex]\frac{6}{1 + 6}[/tex] × 74 ≈ 63

The number of green beads, g, in a belt is therefore;

  • 56 < b < 63

The sum of the beads on each belt = g + b = x

Therefore;

  • 70 < g + b < 74

From the given maximum and minimum ratios, we have;

  • [tex]\underline{\dfrac{1}{4} \leq \dfrac{b}{g} \leq \dfrac{1}{6}}[/tex]

Learn more about inequalities here:

https://brainly.com/question/371134

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.