IN this multiplication problem each letter P, Q and R represents a different digit. What 3 digit number is represented by PQR?
PQR x 3 = QQQ
3xPQR = QQQ = Qx111 ---->
PQR = 37 Q ---->
P0R = 27 Q
You know that 25x4 = 100, so you could try Q = 4, beause you ten get a number slightly larger than 100 which will probably have a zero as the second digit:
27 x 4 = 108
So, Q = 4 and we see that P = 1 and
R = 8.
Since the rightmost digit of the product is always the rightmost digit of the multiplier, R must be 3.
Then $QQQ$ must be divisible by 3, so $Q$ must be one of ${3,6,9}$.
Since $QQQ$ is divisible by 9, $Q=9$.
Then the leftmost digit of the product is the leftmost digit of the multiplier, which is $P$.
Finally, $PQR=\boxed{903}$.
Ah, the beauty of math puzzles! So, we have PQR x 3 = QQQ, and we're trying to find the value of PQR. Let's break it down!
First, we see that Q represents a digit, which when multiplied by 111, gives us QQQ. Well, the only way that Q multiplied by 111 can give us a three-digit number is if Q itself is a number from 1 to 9. We can't have Q as 0 because then QQQ would also be 0.
Now, we move on to PQR = 37Q. Since Q can be any digit from 1 to 9, let's have some fun and try a few numbers. Let's go with Q = 4 just for kicks!
If Q = 4, then PQR = 374. But hold your horses! We need to check if this works with our original equation.
When we multiply 374 by 3, we get 1122, not QQQ. So, 374 is not the correct answer.
Let's keep going till we find the right combination of P, Q, and R.
After some testing, we find that P = 1, Q = 4, and R = 8 works!
So, the three-digit number represented by PQR is 148.
Hope that brings a smile to your face! If you have any more math puzzles or questions, I'm here to clown around and help!
To find the value of PQR, we can use the given information:
PQR x 3 = QQQ
We know that Q = 4, so let's substitute that in:
P4R x 3 = 444
We can rewrite 444 as 4 x 111:
P4R x 3 = 4 x 111
Now let's solve for P4R:
P4R = 4 x 111 / 3
When we divide 4 x 111 by 3, we get 148:
P4R = 148
So, the three-digit number represented by PQR is 148.
To find the value of PQR, we need to solve the equation PQR x 3 = QQQ. However, since P, Q, and R represent different digits, we need to determine the values of each digit.
Let's start by simplifying the equation:
3xPQR = QQQ = Qx111
Since Q is a digit, Qx111 will always result in a three-digit number. Therefore, we can conclude that PQR should also be a three-digit number.
Next, let's break down the equation further:
PQR = 37Q
From the equation, we can see that PQR is divisible by Q. This means that Q must be a factor of PQR. Therefore, we need to find a value of Q that makes PQR divisible by Q.
To find a suitable value for Q, let's consider the equation:
P0R = 27Q
We know that 25x4 equals 100, and since PQR is a three-digit number, we can assume that Q will be slightly larger than 1. Thus, we can try Q = 4, as it will give us a number slightly larger than 100, which will likely have a zero as the second digit.
So, let's see if Q = 4 works:
27 x 4 = 108
From the calculation, we find that Q = 4 yields a valid result. We can then conclude that P = 1 and R = 8.
Therefore, the three-digit number represented by PQR is 148.