Grades 5-6 Video Solutions 2021-video 2021 5-6/24

Video Transcription

Number 24. An apple and an orange weigh as much as a pear and a peach weigh together. An apple and a pear weigh less than an orange and a peach together.  And a pear and an orange weigh less than an apple and a peach together. Which of the pieces of fruit is the heaviest?  Okay, well, what we can do first is we can write down all the equations and the inequalities that we have. An apple and an orange weigh as much as a pear and a peach.  Okay, apple plus orange equals pear plus peach. An apple and a pear weigh less than an orange and a peach together. Okay, apple and a pear is less than an orange and a peach.  And then we have a pear and an orange weigh less than an apple and a peach. Okay, so these are the three equations that we have now. Well, what can we do with these?  Well, we can put them together to get what we need. Let's start with the apple plus pear plus the pear plus orange. So this is the bottom two.  If we add these two inequalities together, we get that apple plus pear plus pear plus orange is less than orange plus peach plus apple plus peach.  Okay, well, we can start canceling things out. We can cancel out this apple. We can cancel out this orange. And now we have that we have two pears left on this side.  We have two peaches left on this side. So two pears is less than two peach. That tells us pear weighs less than a peach. Okay, now we can add apple plus orange plus apple plus pear.  So we're adding these two, the top two. And then we have on this side, pear plus peach plus orange plus peach. Okay, so what can we cancel out here?  Well, we can cancel out this orange. We can cancel out this pear. So we have two apples weigh less than two peaches. That tells us now that apples weigh less than peaches.  Now, finally, we take these, the first and the last. Apple plus orange plus pear plus orange is less than pear plus peach plus apple plus peach.  So pear plus peach plus apple plus peach. Now we can cancel out this apple on both sides. We can cancel out this pear on both sides. And now we have orange.  Two oranges is less than two peaches, which tells us that orange is less than peach.  Okay, well, peach we see that is heavier than orange. It's heavier than apple. It's heavier than pears. So peach is heavier than all the other three.  That means that peach must be the heaviest of these four fruits. The answer, therefore, is C.

Video Summary

The transcript describes a series of weight comparisons among four fruits: apple, orange, pear, and peach. By creating and combining equations and inequalities from these comparisons, it is determined that peach is the heaviest. This conclusion is reached through canceling terms in the equations, showing that peach weighs more than the apple, pear, and orange in each scenario. Therefore, the peach is identified as the heaviest fruit.

Keywords

fruit

weight comparison

peach

equations

inequalities