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The system of inequalities that model the number and types green (g)
and blue (b) beads in a belt are as follows;
- <u>70 < g + b < 74</u>
- <u>10 < g < 14</u>
- <u>56 < b < 63</u>
The waist size for the belt = ±28 inches
The <em>x</em> 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 = = 10
Maximum number of blue beads = ≈ 14
The number of blue beads, <em>b</em>, in a belt is therefore;
- <u>10 < g < 14</u>
<u />
Minimum number of green beads = × 70 = 56
Maximum number of green beads = × 74 ≈ 63
The number of green beads, <em>g</em>, in a belt is therefore;
- <u>56 < b < 63</u>
The sum of the beads on each belt = g + b = x
Therefore;
<u />
- <u>70 < g + b < 74</u>
From the given maximum and minimum ratios, we have;
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