Grades 9-10 Video Solutions 2025-2025_9-10

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Problem 14. Paul shoots a total of 27 times at two targets. He hits 50% of the shots he aims at the top left target, and 80% of the shots he aims at the bottom right target.  He misses a total of 9 shots. How many times did he aim for and hit the top left target? So first, let's just say that L is the number of shots that he made towards the top left  target, and R is the number of shots he made to the bottom right target. We know that L plus R is 27, because he shot a total of 27 times.  Now let's look at how many of the shots he hit. So because he misses a total of 9 shots, he must have made the remaining 27 minus 9, or 18 shots. We can also write this a different  way. We know that he hit 50% of the shots he made at the top left target, which is 50% of L and 80% of R. So we have 50% of L plus 80% of R is 18.  And we can simplify this to half L plus 4 fifths R is 18. Now, we remember that we have our previous equation that L plus R is 27. And so now we have two equations in L plus R,  and we can use them to find L. So instead of R, we can substitute 27 minus L. And this gives us  the equation half L plus 4 fifths times 27 minus L is 18. If we solve, we get that L is 12. Now, the question isn't asking how many shots were aimed at the top left target.  They asked how many times he hit. And we know that he hits 50% of the time when he aims at the top left target. So out of the 12 shots he aimed, he must have made 50%, which is 6.  And so the answer is C.

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