Grades 7-8 Video Solutions 2025-2025_7-8

Video Transcription

Problem number 22. During two sessions of soccer training, Paul shoots a total of 17 times at a target. He hits 60% of the shots he shoots in the first session.  He hits 75% of the shots he shoots in the second session. How many times did he hit the target in the second session?  Let's write some variables representing the number of times Paul shot in the first and second sessions.  a is the number of times he shot in the first session, and b is the number of times in the second session.  Now we know that 3 fifths of a and 3 fourths of b are the number of shots he hit in the first and second sessions respectively,  by converting the percents to fractions, and we know both of those are integer numbers.  This means that a has to be a multiple of 5, and b has to be a multiple of 4 for both of these to be integers.  Now we can try to list all the possibilities for a, since we know a is less than 17. We know that a can be 5, 10, or 15.  Using those values of a, we can find the value of b by doing 17 minus a, and those values of b are 12, 7, or 2.  But remember that b has to be a multiple of 4 for 3 fourths of b to be an integer. So in this case, the only possible multiple of 4 in this list is 12.  And so that means that the number of shots hit in the second session is 3 fourths of 12, which is 9. So the answer is d, 9.

Video Summary

Paul shot at a target 17 times over two soccer sessions. He hit 60% of his shots in the first session and 75% in the second session. Using variables for the sessions (`a` for the first and `b` for the second), we know `a + b = 17`, and `3/5 of a` and `3/4 of b` must be integers. After testing possibilities where `a` is a multiple of 5 and `b` a multiple of 4, only `a = 5` and `b = 12` fit the conditions. Thus, in the second session, Paul hit the target 9 times.