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german
3 years ago
12

Amy's grandmother gave her 3 identical chocolate chip cookies and 4 identical sugar cookies. In how many different orders can Am

y eat the cookies such that either she eats a chocolate chip cookie first, she eats a chocolate chip cookie last, or both?
Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Answer:

chocolate chip cookie first: 15 ways

chocolate chip cookie last: 15 ways

chocolate chip cookie first and last: 5 ways

Step-by-step explanation:

There is a total of 7 cookies.

Is she eats a chocolate cookie first, she will have 2 chocolate cookies and 4 sugar cookies (6 in total).

So, to find the number of different orders that Amy can eat the remaining cookies, we just need to calculate a combination of 6 choose 2 (that is, the number of ways we can put the 2 chocolate cookies among the 6 cookies) or a combination of 6 choose 4 (same thing, but for the sugar cookies):

C(6,2) = 6! / (2! * 4!) = 6 * 5 / 2 = 15 ways

Is she eats a chocolate cookie last, she will have 2 chocolate cookies and 4 sugar cookies (6 in total), so the problem is solved again with a combination of 6 choose 2:

C(6,2) = 15 ways

Is she eats a chocolate cookie first and last, she will have just 1 chocolate cookie left and 4 sugar cookies (5 in total), so the problem is solved with a combination of 5 choose 1 or a combination of 5 choose 4:

C(5,1) = 5! / (1! * 4!) = 5 ways

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48 adult tickets and 24 children tickets were sold.

Step-by-step explanation:

Given,

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Cost of one child ticket = $3

Total worth of sold tickets = $456

Let,

Number of adult tickets sold = x

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According to given statement;

8x+3y=456     Eqn 1

x = 2y              Eqn 2

Putting value of x from Eqn 1 in Eqn 2

8(2y)+3y=456\\16y+3y=456\\19y=456

Dividing both sides by 19

\frac{19y}{19}=\frac{456}{19}\\y=24

Putting y=24 in Eqn 2

x=2(24)\\x=48

48 adult tickets and 24 children tickets were sold.

Keywords: linear equation, substitution method

Learn more about linear equations at:

  • brainly.com/question/11253316
  • brainly.com/question/11258952

#LearnwithBrainly

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