Question

Caitlyn sells her drawings at the county fair. She wants to sell at least 85 drawings and has portraits and landscapes. She sells the portraits for $14 each and the landscapes for $10 each. She needs to sell at least $980 worth of drawings in order to earn a profit.Write a system of 2 inequalities to model this situation. Use "x" for the number of portraits and " y " for the number of landscapes.

Answer 1

Given:

Sell at least 85 drawing.

Sells the protraits for $14 each and landscapes for $10 each worth atlest $980

Find: Write a system inequality

Sol:.

`x+y\ge85`
`14x+10y\ge980`

Graph of inequality is:

(C)

If Caitlyn sells 40 protraits and 50 landscapes is:

`\begin{gathered} 14x+10y\ge980 \\ 14(40)+10(50)=1060 \end{gathered}`
`\begin{gathered} \text{Sales } \\ x+y\ge85 \\ 40+50=90 \end{gathered}`

Yes she meet minimum sale and profit is 1060.

(D)

If Caitlyn sells 80 protraits and 55 landscapes is:

`\begin{gathered} \text{Sales} \\ x+y\ge85 \\ 80+55\ge85 \end{gathered}`
`\begin{gathered} \text{Earn profit} \\ 14x+10y \\ =14(80)+10(55) \\ =1120+550 \\ =1670 \end{gathered}`

Profit 1670 and yes she meet minimum sales.