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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
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