Inequality:
[tex]20a+12b\ge500[/tex]
To know which combination represents a solution, we have to replace the values given and see if the inequality is true.
• 5 necklaces (a) and 40 bracelets (b)
[tex]\begin{gathered} 20\cdot5+12\cdot40\ge500 \\ 100+480\ge500 \\ 580\ge500 \end{gathered}[/tex]
As this condition is TRUE, then 5 necklaces and 40 bracelets is a solution.
• 10 a and 20 b
[tex]\begin{gathered} 20\cdot10+12\cdot20\ge500 \\ 200+240\ge200 \\ 440\ge200 \end{gathered}[/tex]
As this condition is NOT true, then 10 a and 20 b is NOT a solution.
• 15 a and 15 b
[tex]\begin{gathered} 20\cdot15+12\cdot15\ge500 \\ 300+180\ge500 \\ 480\ge500 \end{gathered}[/tex]
As this condition is NOT true, then 15 a and 15 b is NOT a solution.
• 20 a and 10 b
[tex]\begin{gathered} 20\cdot20+12\cdot10\ge500 \\ 400+120\ge500 \\ 520\ge500 \end{gathered}[/tex]
As this condition is TRUE, then 20 a and 10 b is a solution.
Answer (solutions):
• 5 necklaces and 40 bracelets: yes
,
• 10 necklaces and 20 bracelets: no
,
• 15 necklaces and 15 bracelets: no
• 20 necklaces and 10 bracelets: yes
