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Answer 1

The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Given an equation showing profits of A Christmas vendor as

P=-0.1$g^{2}$+30g-1200.

We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.

To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.

665.60=-0.1$g^{2}$+30g-1200

0.1$g^{2}$-30g+1200+665.60=0

0.1$g^{2}$-30g+1865.60=0

Divide the above equation by 0.1.

$g^{2}$-300g+18656=0

Solving for g we get,

g=[300±$\sqrt{(300)^{2}-4*1*18656 }$]/2*1

g=[300±$\sqrt{90000-74624}]/2$

g=[300±$\sqrt{15376}$]/2

g=(300±124)/2

g=(300+124)/2       , g=(300-124)/2

g=424/2,  g=176/2

g=212,88

Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.

Put the value of P=1500 in equation P=-0.1$g^{2}$+30g-1200.

-0.1$g^{2}$+30g-1200=1500

0.1$g^{2}$-30g+1500+1200=0

0.1$g^{2}$-30g+2700=0

Dividing equation by 0.1.

$g^{2}$-300g+27000=0

Solving the equation for finding value of g.

g=[300±$\sqrt{300^{2} -4*1*27000}$]/2*1

=[300±$\sqrt{90000-108000}] /2$

=[300±$\sqrt{-18000}$]/2

Because $\sqrt{-18000}$ comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.

Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Learn more about equation at brainly.com/question/2972832

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