OrangeJuicy

You are currently 13 miles north and 8 miles east from your starting point.

Figuring it out using pythagorean theroem...: sqrt(13^2+8^2), answer = sqrt(233)

By trial and error find the smallest number to satisfy (i) and (ii) is 8.

Then go on by trialing numbers of 8 + 15n since 15 is the least common multiple of 3 and 5. 

You will find the answer to be 68 within just a few tries.

There should be a better and more official way by modulo arithmetic though so it would be great if someone can also add that to this thread.

There are more than one way to tackle this problem but I'll offer my best solution.

Total area of rectangle = 4*5 = 20

Then, subtract the three white parts that are not counted(2*4/2 = 4, 2*3/2 = 3, and 2*5/2 = 5)

Our final answer is 20 - 3 - 4 -5 = 8

The value of your expression is roughly 86.87

so the answer is all integers from -86 to +86, which I'll leave to you to figure out.

The amount of money Andrew starts with we set as X

X - 940 - 5/7(X - 940) + 240 = 2/9X

X- 5/7X -2/9X -940 +4700/7+240 = 0

X-5/7X-2/9X= 940-240-4700/7

4/63X = 200/7

4X = 1800

X = 450????

Can someone check my process because either I made a mistake during calculation or there's something wrong with the question. He can't start with 450 and spend 940.

I answered the question at the original thread, maybe my solution is not the best, but I hope it would be helpful.

This isn't a question that could be solved very easily.

We try to list equations:

G = 1/7(M+K+J)

M = 3/4(K+J)

J = 2/5K

Let's Plug in:

M = 3/4(7/5K) = 21/20K,

G = 1/7(21/20K+K+2/5K) = 1/7(49/20K) = 7/20K

K = K

J = 2/5K

M = 21/20K

G = 7/20K

Now we split all of that $168 into these four parts. 4 parts combined is 56/20K, and thus K original has 168*20/56 = $60. J original has 168*8/56 =  $24

Now you can do the last step: $60 - $X = $24 + $X

Hopefully this proved to be helpful

75workers*4days = 300

50workers*Xdays = 300

that X is the answer

Ernie paints 1/2 a house per hour

Lizzie paints 1/5 of a house per hour

Together they paint  1/5  +  1/2   =  7/10 of a house in an hour

So that is 10/7   hours per house, and that's 20/7 hours for two houses

1024 is 1 more than 512+256+128+64+32+16+8+4+2+1.

It's helpful to notice that every term is 1 more than all the previous terms combined.

Simplify, and get pq^2

OK, so I would set all the money he has at first as X, our variable.

X - 1/3X - 120 = 2/3X - 120 is what he has after sentence 1

1/3(2/3X-120)-120 = 2/9X - 160 is what he has after sentence 2

1/3(2/9X - 160) -120 = 2/27X - 520/3 is what he has after sentence 3, but since by this time he doesn't have any money left, we can infer than

2/27X - 520/3 = 0, thus 2/27X = 520/3.

Find X to get the answer.

We set all the marbles Fred has as X.

We can infer from the first sentence that: X - (1/4X+34) = 3/4X - 34 marbles is what Fred has after the first sentence

Now, 3/4X - 3/8(3/4x - 34) = 3/4X-9/32X+51/4 = 15/32X+51/4 is what he has after the second sentence

That suggests that 15/32X + 51/4 = 580, which means 15/32X = 2551/4, and find X to get the answer to the question.

The smallest common multiples are: 60, 120, 180

Their sum is 360

This question is answered here: https://web2.0calc.com/questions/i-have-tiled-my-square-kitchen-floor-with-congruent-square-tiles-all-the-tiles-are-white-except-those-along-the-two-diagonals-which-are-a