Grades 5-6 Video Solutions 2021-video 2021 5-6/27

Video Transcription

Number 27. Each shelf holds a total of 64 deciliters of apple juice. The bottles have three different sizes, large, medium, and small. How many deciliters of apple juice does a medium bottle contain?  Okay, well what we can do first is we can write out all of the equations. So for the sake of this, we will let L be the large bottles, S be the small, and N be the medium.  And so L basically represents how many deciliters of apple juice is in a large, S is how many deciliters of apple juice is in a small, and M is how many deciliters of apple juice in a medium.  So we have these three equations and three unknowns. If you're familiar with systems of linear equations, this is a solvable system.  So what can we do now? Well, let's look for this pattern. We have 4M plus 6S is 64. Well, over here we have 2M plus 3S plus 2L.  So this is actually half of this value, right? So if we divide all of this equation by 2, we get 2M plus 3S is 32. And then we substitute that in into the second equation.  So now we have 2L plus 32 is 64. That gives us that L has to be 16 deciliters. So now we know the size of a large. But we still don't have everything. We need to find the size of the medium.  Well, we can extend this to the next equation. And this first one has L and S. That's the easiest one to do next. If we say that a large has 16, well, 3 times 16 plus 4S is 64.  3 times 16 is 48. 64 minus 48 is 16. So that tells us the small contains 4 deciliters.  Well, now this becomes a lot easier. We go to the last equation, which only has small and medium. 4M plus 6 times the size of the small, which is 4, is 64. 6 times 4 is 24. 64 minus 24 is 40. 40 divided by 4 is 10. So that tells us that M is equal to 10. Our answer is D.

Video Summary

The transcript describes solving a system of equations to find the volume of a medium bottle of apple juice in deciliters. The problem involves bottles of three sizes: large (L), medium (M), and small (S), with a total shelf capacity of 64 deciliters. By systematically solving these equations, it is determined that a large bottle holds 16 deciliters, and a small bottle holds 4 deciliters. Using these values, the medium bottle's volume (M) is calculated to be 10 deciliters. Thus, the answer is that a medium bottle contains 10 deciliters of apple juice.

Keywords

system of equations

volume calculation

apple juice

bottle sizes

deciliters