If P,Q are digits, 39P * Q3 = 32951, what is value of P + Q?

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owningbro2

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can any one help me with this problem? It states the following:

In the multiplication* shown, P and Q each present a single digit. If the product is 32,951 ; what is the value P + Q?

* this is the multiplication:

3 9 P
X Q 3
------------

please someone help me really fast....Thank you everyone
 
the dots are to line up columns

....39p
..... q3
-------
32,951

the first obvious value is p must be 7, because only 7x3= gives a unit value of 1
p=7
....397
.....q3
-----------
32951

but 397x3= 1191 or 32951-1191=31760

397x10q=31760
397q=3176
q= 3176/397
q=8 answer

Arthur
 
so is the answer 8? i just guessed and checked is it 8? cause thats what i got 8 for Q and P equals 7
 
owningbro2 said:
can any one help me with this problem? It states the following: In the multiplication* shown, P and Q each present a single digit. If the product is 32,951 ; what is the value P + Q? (* this is the multiplication:)

3 9 P
X Q 3
------------

please someone help me really fast....Thank you everyone
Click to expand...

Please show us your work/thoughts so that we know where to begin to help you.

To start - the unit digit of the result (of multiplication) 1

the unit digit of the multiplicand is 3.

There is only one number - when multiplied by 7 - gives you 1 in the unit digit.

What number is that? - P must be that number.

Use similar logic to find Q.
 
arthur ohlsten said:
....but 397x3= 1191 or 32951-1191=31760

397x10q=31760
397q=3176
q= 3176/397
q=8 answer<<< Incorrect
Click to expand...
 
Why can't it be this simple:
since only 3*7 has unit value then 39P = 397;
32951 / 397 = 83 = Q3
 
Denis said:
Why can't it be this simple:
since only 3*7 has unit value then 39P = 397;
32951 / 397 = 83 = Q3
Click to expand...

For this problem - it is that simple.

But some of us tutors - cannot wait to post detailed solution (sometimes wrong solution) - depriving the student from discovering the solution (may be more elegant - like yours).
 
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