Calyley Contest (gr 10) Practice

Thursday March 4th, Mr. Cheng was gone to the Grad retreat with the grade 12's and our math class had Tuesday problem solving day moved to Thursday. We had a choice of choosing past math contests from gr. 9, gr. 10, gr 11 contests. However all of these contests required different numbers questions. For example, gr 9 contest you needed up to 22 questions done, gr 10 contest = 20 questions, gr 11 = 18 questions. So i chose the gr 10 math contest because I will have to take it next year again.

In the practice contest, I really enjoyed solving this one particular problem. It was number 15 in Part B. The question was:

In the multiplication shown, P and Q each represent a single digit, and the product is 32 951. What is the value of P+Q?

3 9 p
x Q 3
----------
____________
3 2 9 5 1

I honestly enjoyed solving this problem because it makes you think. So this is how I solved this problem. So first we have to realize if this question is asking for the sum or the product. Sum means addition and product means multiplication. Anyways, we have to go from right to left and use whatever we have to work with. So 3 x p = something 1. So we have to know what times 3 equals to digit that has the number 1 at the end.
3x1= 1
3x2= 6
3x3= 9
3x4= 12
3x5= 15
3x6= 18
3x7= 21
So we know that we have to multiply 7 to get number 21. Then 3x9 then next, 3x3.

Then the first answer will be
3 9 7
x q 3
---------
1 1 9 1

___________
3 2 9 5 1
Then now we work with the variable q. We know that q has to times 7 and we also know that the product must equal to 5. So we also know that q times 7 must equal to a digit with the last number 6. So this means that 7 x 8= 56. So we try replacing q with 8 .

3 9 7
x 8 3
---------
1 1 9 1
3 1 7 6
________
3 2 9 5 1

So this works. This was how I solved the problem and I really want to have another opportunity to any other similar problem like this.