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Clear explanation! Thanks!

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Correct you are!

Q: Mary has 62 square blue tiles and a number of square red tiles. All tiles are the same size. She makes a rectangle with red tiles inside and blue tiles on the perimeter. What is the largest number of red tiles she could have used?

A:

The more close in number the sides are, the greater the area.

For example, a square of side 5 has a greater area than a rectangle that is 3x7, even though both have the same perimeter.

Since there are four sides, and  \(62\div 4\) equals 15.5, we know that the side lengths is somewhere around the range of 15 to 16.

However, We also need to account for the fact that the corners of the rectangle are overcounted, and since there are 4 corners, we need to add 4 to 62 and get 66.

Now, 66/4 = 16.5, and so the two side lengths are 16 and 17.

Now the part with the red tiles - if the side lengths are 16 by 17, then the area inside creates a 14 by 15 rectangle.

This is because each side has two tiles removed - the two sides.

Try drawing a 5x4 rectangle, and then see what the inside rectangle's dimensions is. It's a 3x2, or 5-2 x 4-2.

The last step is simply to multiply 14 by 15, which gets you 210.

Answer: 210 Red Tiles

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We want the earliest digits to be the biggest. Let's start with 9 since that's the biggest number.

9_____

Now, the only numbers left we can use are 10, 11, 12, etc. all the way to 30.

30 is the biggest one, so let's use that next.

930___

BUT WAIT! There are no digits greater than 30. So let's do 29.

929___

Then 30

92930_

Here, we run into a problem. The last digit must be a single digit, but there is no single-digit remaining. 

If we choose two one-digit numbers in the beginning, then it will work out.

Obviously, 8 and then 9 is the best option.

89____

Then, since 30 cannot be used after these two numbers, we must use 29 and then 30.

Therefore, 892930 is the answer.

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:P

The first person to lose started with $39. The second person to lose started with $21. The third person to lose started with $12.

We can solve this problem by working backwards. After a victory, a winner has double what they started with. As all of the money given to the winners comes from the loser, the loser must have started with the sum of what they have after the game and half of what each winner has after the game.

Let’s label the players P1, P2, and P3, with P1 losing first, P2, losing second, and P3 losing third.

After the third game, we have

P1 has $24

P2 has $24

P3 has $24

As P3 lost, we know P1 and P2 doubled what they had from after the second game, and all of that came from P3. Thus, after the second game, we had

P1 had $24/2 = $12

P2 had $24/2 = $12

P3 had $24 + $12 + $12 = $48

Now, as P2 lost the second game, we know P1 and P3 doubled their totals, and all of that came from P2. Thus, after the first game, we had

P1 had $12/2 = $6

P2 had $12 + $6 + $24 = $42

P3 had $48/2 = $24

Finally, as P1 lost the first game, we know P2 and P3 doubled their totals, and all of that came from P1. So, the starting position was

P1 had $6 + $21 + $12 = $39

P2 had $42/2 = $21

P3 had $24/2 = $12.

This is not from me, all credit goes to Seth Wax from Quora - https://www.quora.com/Three-people-play-a-game-in-which-there-are-always-two-winners-and-one-loser-The-loser-gives-each-winner-an-amount-equal-to-what-the-winner-already-has-After-three-games-each-has-lost-once-and-each-has-24-With-how.

Definition: an amount of money given to local government, an institution, or a particular scholar.

Can you find it now?

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:P

I still remember when I was maybe 3 years old and I had a babysitter who would teach me basic math like 6+8, 5-3, etc.

She told me about multiplication, and I remember saying "I'm never going to understand that!"

If you find something hard at first, when you attack it and learn it, you'll get it!

Well, if you're younger, learning about variables can be really tough.

Geometry and proofs with memorizing theorems is also challenging.

Learning about integrals, derivatives, that stuff in pre-calc is pretty hard (i'm learning this stuff right now)

Depends on your skill level.

Do you know how to distribute?

I think you do, or else you wouldn't get this problem.

Asinus got this correct with a well-thought out explanation, but just if you don't understand distributive, here I am.

3(4x-2y) means 3*4x+3*(-2y). We multiply the outside value, 3, by each term inside the parenthesis.

The equation then becomes \(12x-6y-6x-2y\)

6x-8y.

You are very welcome!

:P