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Aleksandr [31]
3 years ago
14

Cindy has 6 identical pink candies and 8 identical green candies. Find the number of ways that Cindy can line up her candies in

a row, so that there are exactly four places where a pink candy is next to a green candy. One example is $PPGGGPPPGGGGGP.$
Mathematics
1 answer:
Daniel [21]3 years ago
4 0

Answer:

175 ways

Step-by-step explanation:

Form a partition into 2 or 3 parts and the number of ways.

Pink candies

[1,5](2) , [2,4](2) , [3,3](1) , [1,4](3), [1,2,3](6) , [2,2,2](1)

Green candies

[1,7](2) , [2,6](2) , [3,5](2) , [4,4](1) , [1,1,6](3) , [1,2,5](6) , [1,3,4](6) , ,[2,2,4](3) , [2,3,3](3)

Number of ways will be:

(2+2+1) (2+6+6+3+3) + (3+6+1)(2+2+2+1)

Number of ways =( 5×21) + (10×7) = 175ways

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Kamila [148]

Answer:

<em>The cost price of the article was Nu 1,000</em>

<em>The original selling price was Nu 1,120</em>

<em>The second selling price was Nu 1,200</em>

Step-by-step explanation:

<u>System of Equations</u>

Let's call:

x = Original selling price of the article

y = Cost of the article

The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:

0.12y = Original profit

Setting up the equation, we have:

x-y=0.12y

The second condition states the selling price is 80 Nu more than before, that is:

x+80= Second selling price of the article

y = Cost of the article (it doesn't change)

The profit of this condition is 20%, thus:

0.2y = Second profit

This produces a second equation:

x+80-y=0.2y

Let's put both equations together to form a system of equations:

x-y=0.12y

x+80-y=0.2y

Operating on both equations:

x=1.12y

x=1.2y-80

Equating both equations, we have an equation with only y's:

1.12y=1.2y-80

Subtracting 1.2y on each side:

1.12y-1.2y=-80

Operating:

-0.08y=-80

Solving:

\displaystyle y=\frac{-80}{-0.08}=1,000

a)

The cost price of the article was Nu 1,000

b) The selling price of the article will be calculated in both cases:

Original selling price: x=1.12y= 1.12*1000=1,120

The original selling price was Nu 1,120

The second selling price was x+80=1,200

The second selling price was Nu 1,200

8 0
3 years ago
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Hope this helps!
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Answer:

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