Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number 16. A kangaroo jumps up a mountain and then jumps back down along the same route. It covers three times the distance with each downhill jump as it  does with each uphill jump. Going uphill it covers one meter per jump. In total the kangaroo makes 2,024 jumps. What is the total distance in meters that the  kangaroo jumps? So the first thing to do is to assign variables. Let u be the total number of uphill jumps and d the total number of downhill jumps. We  know that the total number of jumps is u plus d equals 2,024 and the total distance is u times 1 plus d times 3. Since we know that each uphill jump  takes 1 meter, each downhill jump is 3 times as long and that will be 3 meters. Now we know that, as mentioned before, the kangaroo will cover three  times the distance with each downhill jump as it does with each uphill jump. So that means that since uphill and downhill is the same distance, it will  take three times as many uphill jumps as downhill jumps. That means that u, the number of uphill jumps, is 3 times d, the number of downhill jumps. We can plug  this back into our first equation and get 3d plus d equals 2,024 or 4d equals 2,024 or d is equal to 2,024 divided by 4 equals 506. Then, since we  know u equals to 3d, we get u equals 3 times 506 equals 1,518. And we want the total distance, so we plug in u and d into our equation from earlier to get  1,518 times 1 plus 506 times 3 which equals 3,036. And so the answer is d, 3,036.

Video Summary

The problem involves a kangaroo that jumps uphill and downhill, with each downhill jump covering three times the distance of an uphill jump. It takes 2,024 jumps in total. By setting variables for uphill (u) and downhill (d) jumps, and knowing each uphill jump is 1 meter while each downhill is 3 meters, we determine that u = 3d because uphill jumps are three times as frequent as downhill jumps. Solving 4d = 2,024 gives d = 506, thus u = 1,518. The total distance is 1,518 meters uphill plus 1,518 meters downhill, totaling 3,036 meters.