Grades 9-10 Video Solutions 2021-video 2021 9-10/5

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Problem number 5 states, the halftime score of a handball match was 9-14, so the visiting team was leading by 5 goals.  After their coach made a change in strategy at halftime, the home team dominated in the second half and scored twice as many goals as their opponents.  The home team won the match by 1 goal. What was the final score of the match? So in this case, we know that the starting score is 9-14, then the away team scored some  points and the home team scored twice as many points as they did. We can say that the away team scored A points and then that the home team must have scored 2 A points.  And in the end, we will say that the away team scored X points. Since the home team won by 1 point, this means that they scored X plus 1.  Now let's see these two alternate types of representing the final score equal to one another. So now we have two equations and two unknown variables, which means we can solve.  We can do this by elimination by subtracting the first equation from the second. We know this will work because the two X's will cancel out. So this is what we get.  X plus 1 minus X equals 9 plus 2A minus 14 plus A. Combine like terms on both sides, the X's cancel on the left as expected and the A's reduce.  Let's add 5 to both sides and we get that A equals 6. If we bring up our original equation now, we can see that the home team scored 2 A points,  so that would be 12, and the away team scored A points, so 6. Plugging A back into our formula, we get a final score of 21 to 20.  Alternatively, this could have been done by constructing a table. Just guess how many points the away team scored and compute the final score from there.  If the home team wins by 1 point, then that's the answer. Otherwise, keep guessing. Strategies like this are quick and dirty when the question is simple but prove less effective  when the problems are more complex. So the problem asked us, what is the final score of the match? The answer is 21 to 20. Letter B.

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