When the remainder theorem is applied to the total number of beads, the number of beads left is 3
The question is an illustration of remainder theorem. Remainder theorem is used to determine the remainder when a number divides another
The number of beads used in each design are given as:
[tex]First = 23[/tex]
[tex]Second = 29[/tex]
[tex]Third = 31[/tex]
Calculate the total number of beads used for all three designs
[tex]Total =First + Second + Third[/tex]
[tex]Total =23 + 29 + 31[/tex]
[tex]Total =83[/tex]
The number of available beads is:
[tex]Available = 750[/tex]
Divide 750 by 83, to get the total number of designs
[tex]n = \frac{750}{83}[/tex]
[tex]n =9.03[/tex]
Remove decimal (do not approximate)
[tex]n = 9[/tex]
The number of beads remaining is calculated using:
[tex]Remaining =Available -n \times Total[/tex]
[tex]Remaining =750 -9 \times 83[/tex]
[tex]Remaining =3[/tex]
Hence, there are 3 beads remaining
Read more about remainder theorem at:
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