in the multiplication:
39P
* Q3
=32951
P and Q each represent a single digit.
what is the value of P+Q?
I may have missed something here, BUT IF the digit is 9, note that 39*9*3*9=9477 which is far short of 32951. And 9 is the largest single digit we have. SO, I think something is not right.
The Question is :
39P
* Q3
=32951
each number is in a box. You are supposed to multipy 3 9 P by Q 3
and get 3 2 9 5 1
and then find the value of P and of Q.
Well, well, well, looks like we stumbled upon a mathematical mystery! Let's put on our detective hats and crack this case.
If we break it down step by step, we'll see that the first digit of the result, 3, must be the result of multiplying the units digits together. So, that means Q multiplied by 3 gives us 3.
Next up, we have the last digit of the result, which is 1. Now, we know that the product of two single digits can't yield a number with two digits, so P multiplied by 3 gives us a number that ends in 1. The only single-digit number that makes this possible is 7 (3 times 7 is 21, which ends in 1).
So far, we have Q = 1 and P = 7.
To get the remaining digits in the result, we multiply the tens and hundreds digits of the multiplicands. Now, we have 9P multiplied by Q. We already know that P is 7, so let's plug it in:
9 x 7 = 63
Since we know that the result ends in 1, we can deduce that multiplying 3 by Q must give us a number that ends in 1. The only single-digit number that fits the bill is 7.
Therefore, Q must equal 7.
Finally, let's check our solution:
397 multiplied by 73 does indeed give us 32,951.
So, P + Q equals 7 + 7, which is 14.
So, the value of P + Q is 14. Case closed, my mathematical friend!
To find the value of P and Q, we can break down the multiplication problem step by step.
The given problem is:
39P
* Q3
= 32951
Let's start by multiplying the digits in the ones place:
3 * P = 3P
Next, we multiply the digits in the tens place:
9 * P = 9P
Now, let's multiply the digits in the hundreds place:
3 * Q = 3Q
To determine the value of P and Q, we need to examine the result on the right side of the equation, which is 32951.
From here, we can deduce the following:
- Since the last digit in the product 3Q is 1, Q must be 7. (because 3 * 7 = 21)
- Now we can subtract the value of 3Q (3 * 7 = 21) from the right side of the equation, which is 32951, to obtain the remaining digits: 32951 - 21 = 32930.
- Since the remaining digits are 3293P, we can deduce that P must be 0 because 32930 does not end with 0.
Therefore, the value of P is 0 and the value of Q is 7.
To find the value of P + Q, we can simply add P and Q:
0 + 7 = 7.
Hence, the value of P + Q is 7.
To find the value of P and Q in the multiplication problem, we need to follow the steps provided.
Step 1: Analyze the given multiplication problem.
The multiplication problem is shown as:
39P
* Q3
= 32951
Step 2: Multiply the two numbers horizontally, starting from the rightmost digit.
Multiply the units digit of the top number (P) with the 3 in the bottom number. The result should be the rightmost digit of the product, which is 1. Therefore, P * 3 = 1.
Step 3: Carry over any additional numbers to the left.
Since the product of P and 3 is a single-digit number, there is no need to carry over any numbers.
Step 4: Multiply the tens digit of the top number (9) with the Q in the bottom number.
Multiply 9 by Q, and the result should be the second rightmost digit of the product. Now, we have the equation: (9 * Q) * 10 + 1 = 32951.
Step 5: Solve the equation.
To find the value of Q, we can manipulate the equation to isolate Q. So, we have (9 * Q) * 10 + 1 = 32951. Subtract 1 from both sides of the equation to get (9 * Q) * 10 = 32950. Then, divide both sides by 10 to get 9 * Q = 3295.
Step 6: Find the value of Q.
Now, divide 3295 by 9, and we get Q = 366.11. Since Q is a single digit, we can conclude that Q equals 6.
Step 7: Find the value of P.
Using the equation P * 3 = 1, we divide 1 by 3 to get P = 0.33. However, the given problem states that P and Q each represent a single digit. Therefore, P must be 0.
Step 8: Determine the value of P + Q.
P = 0 and Q = 6, so P + Q = 0 + 6 = 6.
In summary, the value of P is 0, the value of Q is 6, and the sum of P + Q is 6.