
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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February 18th, 2019, 10:50 AM  #1 
Newbie Joined: Feb 2019 From: Britain Posts: 2 Thanks: 0  Coke Bottles!
Samantha bought bottles of Coke on a monthly basis. One month, she got 45 cents change from a 5 dollar bill note. The next month, there had been a price rise. This time, she got 50 cents change. How many bottles did she buy each time and what was the price?(At the time, Coke cost between 60 and 80 cents per bottle.)

February 18th, 2019, 12:11 PM  #2 
Newbie Joined: Jul 2018 From: Georgia Posts: 28 Thanks: 7 
The first time she bought 7 bottles at 65 cents each. The second time, 6 bottles at 75 cents each. 
February 18th, 2019, 12:13 PM  #3 
Newbie Joined: Feb 2019 From: London Posts: 7 Thanks: 0  
February 18th, 2019, 12:33 PM  #4 
Senior Member Joined: Nov 2015 From: United States of America Posts: 195 Thanks: 25 Math Focus: Calculus and Physics  
February 18th, 2019, 01:28 PM  #5 
Newbie Joined: Jul 2018 From: Georgia Posts: 28 Thanks: 7 
Well, a bit of trial and error but there is a way to narrow it down pretty quickly. The first total cost ($4.55) had to be a number divisible by 5, so the cost had to be divisible by five and the number of bottles had to be odd. The only two possibilities for the cost in that range are 65 and 75. A quick mental calculation will show that 9 times either of those is too much (9 x 60 is 540) and 5 times either of them is too little (5 x 70 is 350), so the number of bottles is 7 and by the same method you can quickly eliminate 75 as a price. Then for the second one, you know the product of bottles x price has to be very close to the first calculation and either the number of bottles must be even or the price must be divisible by 10. Think about it a bit more. The first calculation expands to (7 x 60) + (7 x 5). So... easy to see that: (6 x 70) + (6 x 5) is 5 cents less. I'm sure somebody can formalize that better than I did. Edit: Sorry  in the first sentence I should have said 'an odd number divisible by 5' not just 'a number divisible by 5.' Last edited by RichardJ; February 18th, 2019 at 01:37 PM. 

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