Grades 5-6 Video Solutions 2025-2025_5-6

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Number 29. Sarah had three times as many chocolate bars as Sanaz. Sarah then gave a quarter of her bars to Sanaz. Now Sarah has six more bars than Sanaz.  How many more bars than Sanaz did Sarah have originally? Pause if you want to try and solve it.  Okay, so for this one, it helps to use a variable. So let's call the number of bars that Sanaz had X. Then the number that Sarah had is three times as many. So Sarah has three X.  So now Sarah gives a quarter of her bars to Sanaz. Well, one quarter of three X is actually X, it's three quarters X, right? Three divided by four, three quarters.  So X, Sanaz now has X plus three quarters X.  And Sarah has three minus three quarters X. And that's going to be equal to two and one quarter X.  All right, and now Sarah has six more bars than Sanaz.  So what we can do is write these as improper fractions, X plus three quarters X is going to be seven quarters X, if we write it as an improper fraction.  And two and one quarter X, we can write as nine quarters X,  because two is eight quarters plus one is nine quarters X.  And so Sarah has six more than Sanaz. So nine quarters X minus seven quarters X is equal to six. So nine quarters minus seven quarters  is equal to two quarters, which is equal to one half. So one half X is equal to six.  So that means that X is, I'm writing backwards here, X is equal to 12. So if X is 12, then the difference between what Sarah had originally, which was three X,  and what Sanaz had originally was X. So three X minus X is two X. So two X is equal to 24. So Sarah had 24 more bars than Sanaz originally. That is option D.

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