Question

3. The profit from selling vitamin X is$5.00 a bottle. The profit from sellingvitamin Y is $6.00 a bottle. Which ofthe following combinations of salesgives a profit of at least 42.00?A. 5 bottles of X and 2 bottles of yB. 1 bottle of X and 5 bottles of YC. 4 bottles of X and 4 bottles of YD. 6 bottles of y none of XE. 7 bottles of brand X none of Y

Answer 1

Let:

Yx = Profit from selling vitamin X

Yy = Profit from selling vitamin Y

x = Number of bottles

Those profits are given by:

`\begin{gathered} Yx=5x \\ Yy=6x \end{gathered}`

Therefore, for a profit of at least 42.00:

`\begin{gathered} Yx+Yy\ge42.00 \\ 5x+6x\ge42 \end{gathered}`

Let's check every option:

A.

`\begin{gathered} 5(5)+6(2)\ge42 \\ 37\ge42 \\ _{\text{ }}False \end{gathered}`

This is not a valid option.

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B.

`\begin{gathered} 5(1)+6(5)\ge42 \\ 35\ge42 \\ _{\text{ }}False \end{gathered}`

This is not a valid option

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C.

`\begin{gathered} 5(4)+6(4)\ge42 \\ 44\ge42 \\ _{\text{ }}True \end{gathered}`

This is a valid option:

Answer:

C. 4 bottles of X and 4 bottles of Y