Answer: See Below
Step-by-step explanation:
(b) Make a table of white ovals and black ovals. You will notice that
white starts with 3 and adds 3 to each design → 3 + 3(d - 1) = 3d
black starts with 4 and adds 4 to each design → 4 + 4(d - 1) = 4d
[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\text{white ovals}}&\underline{\text{black ovals}}\\1&3&4\\2&6&8\\3&9&12\\4&3(4)=12&4(4)=16\\5&3(5)=15&4(5)=20\\6&3(6)=18&4(6)=24\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&3n&4n\end{array}[/tex]
white ovals when design = 30 ---> 3d = 3(30) = 90
black ovals when design = 100 ---> 4d = 4(100) = 400
white ovals when design = 50 ---> 3d = 3(50) = 150
black ovals when design = 50 ---> 4d = 4(50) = 200
TOTAL = 350
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(c) Make a table of rods and squares. You will notice that
rods start with 19 and add 12 to each design → 19 + 12(d - 1) = 12d - 7
squares start with 6 and add 4 to each design → 6 + 4(d - 1) = 4d + 2
[tex]\begin{array}{c|c|c}\underline{\text{Design \#}}&\underline{\qquad \text{rods}\qquad }&\underline{\qquad \text{squares}\qquad }\\1&19&6\\2&31&10\\3&43&14\\4&12(4)-7=55&4(4)+2=18\\5&12(5)-7=67&4(5)+2=22\\6&12(6)-7=79&4(6)+2=26\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\\cdot&\cdot&\cdot\\n&12n-7&4n+2\end{array}[/tex]
rods when design = 15 ---> 12d - 7 = 12(15) - 7 = 173
squares when design = 15 ---> 4d + 2 = 4(15) + 2 = 62
