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Citrus2011 [14]
3 years ago
7

At a large picnic, there were 45 dishes served altogether. Every 3 people shared a dish of Cole slaw between them. Every 4 peopl

e shared a dish of potato salad between them. Every 6 people shared a dish of hot dogs between them. How many people were at the picnic?
Mathematics
1 answer:
erik [133]3 years ago
6 0

Answer:

There were 12·5=60 people at the picnic.

Step-by-step explanation:

If every 3 people shared a dish of Cole slaw between them, every 4 people shared a dish of potato salad between them and every 6 people shared a dish of hot dogs between them, then you can find the minimal number of people that can do such thing. Mathematically this is the least common multiplier LCM.

Since

  • 3=3;
  • 4=2·2;
  • 6=2·3,

then LCM(3,4,6)=2·2·3=12.

Suppose at the picnic were 12 people. If every 3 people shared a dish of Cole slaw between them, then 12 : 3 = 4 such dishes were served. If every 4 people shared a dish of potato salad between them, then 12 : 4 = 3 such dishes were served. If every 6 people shared a dish of hot dogs between them, then 12 : 6 = 2 such dishes were served. In total, 4 + 3 + 2 =9 dishes.

You know there were 45 dishes served altogether. 45 is 5 times more than 9, then the number of people at the picnic is 5 times  more than 12. Therefore, there were 12·5=60 people at the picnic.

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Answer: ⇒ x

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Step-by-step explanation:

First you had to add by 2 from both sides of equation.

x-2+2>2x+12+2

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Then you had to subtract by 2x from both sides of equation.

x-2x>2x+14-2x

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(-x)(-1)

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x

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Hope this helps!

Thank you for posting your question at here on brainly.

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Answer:

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Step-by-step explanation:

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Read 2 more answers
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Stella [2.4K]

Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

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Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

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Let's try the second example:

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Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

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The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )

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