Question

Tia sells her jewelry online. She sells necklaces for $20 each and bracelets for $12 each. The inequality represents her monthly needs.

Answer 1

Inequality:

`20a+12b\ge500`

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)

`\begin{gathered} 20\cdot5+12\cdot40\ge500 \\ 100+480\ge500 \\ 580\ge500 \end{gathered}`

As this condition is TRUE, then 5 necklaces and 40 bracelets is a solution.

• 10 a and 20 b

`\begin{gathered} 20\cdot10+12\cdot20\ge500 \\ 200+240\ge200 \\ 440\ge200 \end{gathered}`

As this condition is NOT true, then 10 a and 20 b is NOT a solution.

• 15 a and 15 b

`\begin{gathered} 20\cdot15+12\cdot15\ge500 \\ 300+180\ge500 \\ 480\ge500 \end{gathered}`

As this condition is NOT true, then 15 a and 15 b is NOT a solution.

• 20 a and 10 b

`\begin{gathered} 20\cdot20+12\cdot10\ge500 \\ 400+120\ge500 \\ 520\ge500 \end{gathered}`

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