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A group of artists is selling small prints to raise money for charity. They sell p prints, and make a profit of f(p) on the sales. If f(p) = 17p − 340, which statement is true? A. If the group sells 12 prints, they will lose $204. B. If the group sells 28 prints, they will lose $136. C. If the group sells 35 prints, they will make $935. D. If the group sells 15 prints, they will lose $85.

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mathjohndough

The correct answer is is D) If the group sells 15 prints they will loose $85.

To figure out which statement is true, we have to evaluate the function ,

[tex]p(x)=17x-340[/tex] for all the values given in options (A)-(D).  A negative output represents a loss and  a positive output will represent a profit.

In A [tex]p=12[/tex] so [tex]f(12)=17\times 12-340=-136[/tex]. In this case we gather that if they sell 12 prints, they will make a loss of $136. This tells us that option A is wrong.

In B, [tex]p=28[/tex] so [tex]f(28)=17\times 28-340=136[/tex]. In this case we gather that if they sell 28 prints, they make a profit of $136. This tells us that option  B is wrong.

In C, [tex]p=35[/tex] so [tex]f(35)=17\times 35-340=225[/tex]. In this case we gather that if they sell 35 prints, they make a profit of $225. This tells us that option  C is wrong.

Lastly, [tex]p=15[/tex] so [tex]f(15)=17\times 15-340=-85[/tex]. In this case we gather that if they sell 28 prints, they make a loss of 85 dollars. From this we gather that D is the correct option.

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