Sal adds to find the total value when given an amount US dollars.
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- You have in front of you 435 five-dollar bills and 855 ten-dollar bills. Your problem: Place the five-dollar bills and the ten-dollar bills in stacks so that each stack has the same number of bills, and each stack contains only one kind of bill (five-dollar or ten-dollar). What is the largest number of bills that you can place in each stack?(14 votes)
- The number of bills in each stack must be a common factor of the number of $5 bills, 435, and the number of $10 bills, 855. So the largest number of bills in each stack is the greatest common factor of 435 and 855. (Note that the actual values of the bills, $5 and $10, do not matter in this problem. What matters is that the bills are of two different kinds.)
The prime factorization of 435 is 3*5*29.
The prime factorization of 855 is 3*3*5*19.
When we construct the greatest common factor (GCF), we use each possible prime factor the smallest number of times it occurs in any prime factorization.
The prime factor 3 is used once and twice in the prime factorizations, so we use it once in the GCF.
The prime factor 5 is used once and once in the prime factorizations, so we use it once in the GCF.
The prime factor 19 is used zero times and once in the prime factorizations, so we use it zero times in the GCF.
The prime factor 29 is used once and zero times in the prime factorizations, so we use it zero times in the GCF.
So the GCF is 3*5, which is 15. Therefore, the greatest number of bills in each stack is 15.
Have a blessed, wonderful day!(12 votes)
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- [Voiceover] Zhang Tao has two one dollar bills. So two one dollar bills. So let's just write that as one plus one, because each one dollar bill represents one dollar. So, one dollar plus one dollar. That's the two one dollar bills. One five dollar bill. One five dollar bill. So that represents five dollars. And three 10 dollar bills. Three 10 dollar bills. So that's plus ten plus ten plus ten. How much money does he have in all? Well, let's see. One plus, let's see if we can calculate it. One plus one is two. Two plus five is seven. So, these are going to be seven dollars. And then 10 plus 10 plus 10, that's three 10's. So that's going to be 30 dollars. Now what's seven ones plus three 10's? Or what's seven plus 30? Well, that's going to be 37 dollars. So Zhang Tao has 37 dollars in all. Let's do another one of these. Diya has six one dollar bills. And actually, let's draw it out. Diya has six one dollar bills. So that's one, two, three, four, five and six. And these are one dollar bills. So, one dollar bills. This is my rough drawing of one dollar bills. Have to draw a lot of one dollar bills here. So, she has six one dollar bills. She has three five dollar bills. Can we do that in a different color? So, three five dollar bills. So one, so that's a five dollar bill. Two, that's a five dollar bill. And three five dollar bills. That little circle in .... That's supposed to be the picture of someone. Let me make it clear these are pictures of folks. Of famous historical figures. So, these are pictures of famous historical figures here. And then finally she has one 10 dollar bill. One 10 dollar bill. So one 10 dollar bill. So it's worth 10 dollars. A picture of a famous historical figure right over there. So, how much money does she have in all? Well, the six one dollar bills that's going to be six dollars. The three five dollar bills that's going to be worth five, 10, 15 dollars. So plus 15 dollars. And then the one 10 dollar bill. That's going to be worth 10 dollars. 10 dollars. So, what's six plus 15 plus 10? Well, let's see, six plus fifteen is going to be 21. 21 plus 10 is going to be equal to 31 dollars. Is equal to 31 dollars. And you could have also added it this way, You could have said 15 plus 10 plus 10 plus six plus six. Add them together and we would have gotten five plus zero plus six is 11. That's one one and one 10. And then you have three 10's here. So, 31 dollars.