Recently, I completed the 2006 Pascal (grade 9) Contest for fun. This was a question that looked really hard when I first read it, but I figured it out really quickly. Let me show you!
19. The sum of ten consecutive integers is S. Ten times the smallest of these integers is T. What is the value of S-T?
A.) 45 B.) 55 C.) 10 D.) 9 E.) 66
To solve this question, I made an equation of it. First, let the smallest integer be x. This will be what the first equation looks like: x+(x+1)+(x+2)+..........(x+9) = S In total, that would be: 10x+9=S. T would be 10 times the smallest integer, and T would be 10x. To figure this out, you just take away (10x+9) - 10x. Simply the answer would be D.) 9. My reflection on this contest and the problem solving was that it was quite easy, partly because I am in grade 10 and this is a grade 9 contest, but also because I have improved a lot since the last time. I have done a lot more different problems and figured out more different ways to solve them. I feel that now I can solve almost any problem.
Showing posts with label fun. Show all posts
Showing posts with label fun. Show all posts
Friday, March 5, 2010
Thursday, February 25, 2010
Problem Solving #2
This is one of my favorite questions from the second problem solving sheet that I got:
10. If x + y + z = 25 and y + z = 14, then x is:
A.) 8 B.) 11 C.) 6 D.) -6 E.) 31
This question was actually quite simple. Because you know that y and x are equal to 14, you can plug that into the first equation. You can replace (y+z) with 14 to get this equation:
x + 14 = 25
From there, you can easily solve the equation and get the answer B.) 11. One year ago, I wouldn't have been able to solve this question. But now that I have learned to use equations to solve equations, it is much easier. Another way you could solve this problem is guess and check, but that would take forever. I really enjoy problem solving because you never know what kind of problems you are going to get. There are thousands of problems out there just waiting for you to solve them. I especially like problems that you can apply in real life because they are very useful and the skills you pick up are essential. I hope to do more problem solving and get better at it!
10. If x + y + z = 25 and y + z = 14, then x is:
A.) 8 B.) 11 C.) 6 D.) -6 E.) 31
This question was actually quite simple. Because you know that y and x are equal to 14, you can plug that into the first equation. You can replace (y+z) with 14 to get this equation:
x + 14 = 25
From there, you can easily solve the equation and get the answer B.) 11. One year ago, I wouldn't have been able to solve this question. But now that I have learned to use equations to solve equations, it is much easier. Another way you could solve this problem is guess and check, but that would take forever. I really enjoy problem solving because you never know what kind of problems you are going to get. There are thousands of problems out there just waiting for you to solve them. I especially like problems that you can apply in real life because they are very useful and the skills you pick up are essential. I hope to do more problem solving and get better at it!
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