Justin, Alexander, Benjamin, Jordan, and Zachary each had a different amount of money. They all went to the mall and brought their money. At the mall, each person spent a fraction of the money they started out with. They started out with: $48, $60, $96, $12, and $72. At the mall one spent 5/6 of their money, one spent 1/2 of their money, one spent 1/12 of their money, one spent 11/12 of their money, and one spent 1/3 of their money. How much money did each person spend at the mall? How much money does each person have left?
1. Justin has $24 left after spending money at the mall.
2. Benjamin spent $8.
3. Jordan spent less than 1/2 of his money.
4. Zachary did not spend 1/12 of his money.
5. Jordan spent $24.
6. The person that started out with $12, has $2 left after shopping.
+1632 First let's consider the person who had 12$ to start with. If he had 2$ left, that means he spent 5/6th of his money, which you can cross of that option now. You can also cross out the 12$ option for the quantity people start off with. Taking a look at the clues, Alexander is the only person not included, so this person is Alexander. Then Alexander spent 10$ at the mall, and has 2$ left.
Now we consider Jordan. If we know jordan spent 24$, then taking a look at the options for how much people started with, we can see Jordan spent either 1/3 of his money or 1/2 of his money. 11/12 and 1/12 would not be valid options or else Jordan would have too much or too little money in the list of money you start off with. But we are also given Jordan spent LESS than 1/2 of his money, meaning Jordan could only have spent 1/3 of his money. 24 x 3 = 72, so Jordan had 72$ to begin with. Then Jordan spent 24$ at the mall and he has 48$ left.
Now we consider Justin. If Justin had 24$ left after spending money, then Justin either spent 1/12, 11/12, or 1/2 of his money. But if he spent 1/12 or 11/12 of his money, he would either have too much or too little money to begin with. Then the last option is 1/2, so he spent 1/2 of his money, meaning Justin started off with 48$. Then Justin spent 24$ at the mall and he has 24$ left.
Now we consider Benjamin. If Benjamin spent 8$ at the mall, that means he either spent 1/12 or 11/12 of his money. If he spent 11/12 of his money, that means he didn't have a whole number amount of money to begin with, and that isn't an option on the list. Therefore he spent 1/12 of his money, meaning Benjamin started off with 96$. Then Benjamin spent 8$ at the mall and he has 88$ left.
Now we consider Zachary. We know he has spent 11/12 of his money because that is the last option. The last option for money to start off with is 60$, so we now know Zachary spent 11/12 of his money and had 60$ to start. Then Zachary spent 55$ at the mall, and has 5$ left.
Good question!
