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2 years ago

8

Mathematics

1 answer:

Alik [6]2 years ago

3 0

Answer:

Step-by-step explanation:

To solve this we will rewrite the word problem as an equation...

5x (A)

x (B)

When Teddy moves 82 pens from A to B, he is subtracting 82 pens from Box A and adding 82 pens to Box B...

5x - 82 (Change in Box A - subtraction)

x + 82 (Change in Box B - addition)

The problem now states that Box A and Box B are equal...

5x - 82 = x + 82

--- subtract x from both sides ---

4x - 82 = 82

--- add 82 to both sides ---

4x = 164

--- divide both sides by 4 ---

x = 41 pens

Now, we replace the x in the expression "5x - 82" with 41...

5(41) - 82 = 205 - 82

205 - 82 = 123

123 pens in Box A

Hope this Helps!

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Side note: we can prove the triangles to be similar using the AA (angle angle) similarity theorem. The first pair of angles are the vertical angles DOC and BOA which are congruent to each other.The second pair is CDB and ABD which are congruent by the alternate interior angle theorem. Check out the attached image for a visual.

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3 years ago

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You have not given the data for which you like to find the median.

I will however explain how you can find the median of a given set of data, and you can apply the same method to your problem.

Step-by-step explanation:

Median, just like it sounds, is simply the middle value of a given set of data.

Given a set of numbers:

a, b, c, d, e, ..., z.

To find the median, first,

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- Count the whole numbers, if it is odd, you have a middle number, and that is the median.

If it is even, you have two middle numbers, then the median will be the addition of those two numbers divided by two.

Example: To find the median of

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First, we arrange in ascending:

1, 2, 2, 3, 4, 5, 5, 6, 7

Next, we locate the middle number(s), which is 4.

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Example 2: To find the median of

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First, we arrange in ascending:

1, 2, 2, 3, 4, 5, 5, 6, 7, 9

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