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alexandr1967 [171]
3 years ago
7

At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is $14 and the price for 2 cheeseburgers and 4 cups of

lemonade is $12. How much does it cost for 1 cheeseburger and 2 cups of lemonade?
Mathematics
2 answers:
tester [92]3 years ago
7 0
14 dollars= 3 cheeseburger plus 2 cups of lemonade
14=3[4]+2[1]=14
1 cheeseburger= 4 dollars
1 lemonade= 1 dollars
12 dollars= 2cheeseburger plus 4 cups of lemonade

crimeas [40]3 years ago
6 0
C= the price of a cheeseburger and l = the price of a lemonade:

3c + 2l=14\\2c+4l=12

Divide the second equation by -2 to begin the process of solving by elimination:

3c + 2l=14\\-1/2\ (2c+4l=12)\\\\3c+2l=14\\-c-2l=-6\\\\2c=8\\c=4

Now that we have c, 4, we can plug it in to one of the equations to find l:

3c + 2l=14\\3(4)+2l=14\\12+2l=14\\2l=2\\l=1

So, each cheeseburger is $4 and each lemonade is $1.  The final answer is:

1 cheeseburger and 2 cups of lemonade would cost $6.
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There are 50 runners in a race. How many ways can the runners finish first, second, and third?
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Number of ways can the runners finish first, second, and third is 1,17,600 .

<u>Step-by-step explanation:</u>

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is : P(n,r) = \frac{n!}{(n-r)!} where n is the number of things to choose from,  and we choose r of them,  no repetitions,  order matters. Here , n = 50 , r= 3

⇒ P(n,r) = \frac{n!}{(n-r)!}

⇒ P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}

⇒ P(50,3) = 50(49)(48)

⇒ P(50,3) = 1,17,600

∴ Number of ways can the runners finish first, second, and third is 1,17,600 .

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