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3 years ago

14

A store manager wants to have a sales promotion where he gives prizes to the first several people through the door. The manager

wants each person to receive the exact same items and in the same amount. He also wants to distribute all of the prizes. The manager has 280 pins, 200 ornaments, and 60 mugs to distribute.
If the manager wants to give prizes to as many people as possible, how many people will get gifts?

80
4,200
20
200

1 answer:

RUDIKE [14]3 years ago

3 0

20 because it is the greatest common factor

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A caterer provides a conference banquet for a price of $40 per person for 20 or fewer people but will decrease the price by $1 p

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Answer:

The maximum revenue is $900, obtained with 30 people

Step-by-step explanation:

Naturally, the answer should be a number equal or higher than 20, because up to 20 persons, each one pays the same. Lets define a revenue function for x greater than or equal to 20.

f(x) = x*(40-(x-20)) = -x²+60x

Note that f multiplies the number of persons by how much would they pay (here, assuming that there are more than 20).

f is quadratic with negative main coefficient and its maximum value will be reached at the vertex.

The value of the x coordinate of the vertex is -b/2a = -60/-2 = 30

for x = 30, f(x) = 30*(40-(30-20))=30*30=900

So the maximum revenue is $900.

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Answer:

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Step-by-step explanation:

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Solve the inequality for 4(x+1)<-6

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How many solutions does the system of equations below have?

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One solution

Step-by-step explanation:

5x + y = 8

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Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

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$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

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Step-by-step explanation:

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