NotThatSmart

Looks like we got the same answers! AUnverifiedTaxPayer!

Nice work! :)

Also, I accidentally labeled #4 as #3. My bad. 

5. I THINK this is the solution. Unless,umm..idk

The old man temporarily added his dog to the 17, making a total of 18 dogs.

First son got 1/2 of 18 = \(1/2\cdot 18 = 9\)

Second son got 1/3 of 18 = \(1/3 \cdot 18=6\)

Third son got 1/9 of 18  = \(1/9 \cdot 18 = 2\) for a total of 17.

Then I think the old man stole his dog back...so yay?

Nice questions! I might not answer them every week, but it sure was a nice little brain teaser!

Thanks! ::)

3. First, let's note that If any number LQ is multiplied by 9, right most digit of the product will be (10 - Q).

So, from JKL/9 = LQ, we get, L = 10 - Q

LQ can be mathematically represented as\(10L + Q = 10(10 - Q) + Q = 100 - 9Q \)

Since \(PQR/6 = LQ\), \(PQR = 6LQ = 6(100 - 9Q) = 600 - 54Q\)

We now try various values for Q such as 1, 2, 3, .... , etc, till the middle digit of the product turns out to be the same as the value of Q used. We get the correct answer for Q at the very third attempt, namely 3. Hence,

\(L= 10 - 3 = 7\)

So we finally have

\(219/3 = 73 \\ 438/6 = 73 \\ 657/9 = 73\)

Thanks! :)

3. My logic for this problem might be flawed, but let me give it my best shot. 

If One side of the bottom layer of a triangular pyramid has 11 balls, 

The first layer has 1 ball

The Second layer will have \(3 = (1 + 2) \)balls

The Third layer will have \(6=(1 + 2 + 3)\) balls.

The Fourth layer has\( 10=(1 + 2 + 3 + 4)\) balls.

The Fifth layer will have \(15=(1 + 2 + 3 + 4 + 5)\) balls

The sixth layer there are\( 21=(1 + 2 + 3 + 4 + 5 + 6)\) balls

So there will be \(28,36,45,55 \quad \text{and} \quad 66 \) balls in the remaining layers.

So, adding the total number of balls up, we get

\(1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 = 286 balls.\)

So 286 is the answer. 

Again, not sure about this one, should be right. 

Thanks! :)

2. Note that if Harry Puttar (nice name LOL) refills 2 litres and drinks 3 litres, he will drink 1 litre of milk every single day. 

Thus, he should run out of milk by the 40th day. 

The number of litres he drank can be calculated with the sequence

\(1+2+3+4+5+6+...+39+40 = 820\)

Of these total 820 litres, there WAS 40 litres of milk,  meaning he drank

\(820-40 = 780\)litres of water. 

So 780 is our answer. 

Thanks! :)

1. Alright, let's give this a shot. First off, there are 4 prime numbers between 1 and 10. 

We have \(2,3,5,7\)

However, since the product of these two prime numbers must be less than 10 (single digit number), the only two numbers that qualify is \(2 \cdot 3 = 6\)

So now, we have two different numbers to work with. \(263, 362\)

Since their the reverses, take the larger number, 362 is the original. 

We find that \(362-263=99\), meaning we found our number. 

Adding the digits up, we get

\(2+6+3 = 11\)

So 11 is our answer. 

Thanks! :)

It's the same number of painters, all painting at the    

same rate that they painted the 2000 sqft wall.  

The only thing that's different is that the new wall is    

3 times as big, so it will take 3 times as long to paint.   

\(3 \cdot 40 =  120 \) minutes to paint

Thanks! :)

.

WAIT A SECOND! Let's note something real quick. 

First, let's look at the first equation. We want only two equations, we isolate p in terms of r. 

We get that

\(p=3+2q\)

Subsituting this value of p into the second and third equation, we get the system with r and q, we get

\(q-2r=-2+q\\ 3+2q+r=9+3+2q\)

Now, focusing on the first equation of the new system, isolating r, we find that

\(r=1\)

Plugging in this value for r into the second equation, we have that

\(3+2q+1=2q+12\\2q+4=2q+12\\-8=0\)

THIS IS DEFINITELY NOT TRUE. 

In conclusion, we know that this system has NO SOLUTIONS. 

I think this is right...

Thanks! :)

Let's set up a system of equations to solve this problem. 

Let's let b be bagels

Let's let t be toast

And let's let m be muffins. 

From the problem, we have the system

\(2T + 1B = 3.15 \\ 1M + 1B = 3.50 \\ 1T + 2B + 3M = 8.15\)

Now, we want everything to be in terms of bagels. 

From the first two equations, we get the equations

\([3.15 - B ] / 2 = T \\ M = 3.50 - B\)

Now, plugging these values into the third equation, we get

\([ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.62\)

This is 262 cents or about 261 and 2/3 cents. 

Thanks! :)