Christmas Streak 47/88: Diophantine #1
Tom is going to buy some tomatoes and carrots with $31.
A tomato costs $4, and a carrot costs $5.
Given that Tom has to use all of his money, how many tomatoes should he buy?
This problem is a part of <Christmas Streak 2017> series .
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3 solutions
Tomato = x , carrot = y .
4 x + 5 y = 3 1
If x = 0 , then y = 5 3 1 .
If x = 1 , then y = 5 2 7 .
If x = 2 , then y = 5 2 3 .
If x = 3 , then y = 5 1 9 .
If x = 4 , then y = 3 .
x = 5 ⇒ y = 5 1 1 x = 6 ⇒ y = 5 7 x = 7 ⇒ y = 5 3 x = 8 ⇒ y = − 5 2
Therefore, the only value possible for x is 4 .
try to break 31 in form 5x+4y by trying different values of x or y therefore answer is 4
yes that is exactly what I did. For these easy problems that is faster
31 isn’t a multiple of 5. My approach was to think about just that one, because 30 is a multiple of five. So basically 5 + 4 x = 1 ( m o d 1 0 ) and the answer is 4.