Wikipedia:Reference desk/Archives/Mathematics/2019 June 22
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June 22
editQuestion about ratio problems
editIf Tree A produces 7,7kg of fruit and Tree B produces 5,1kg of fruit per year and 1 year 112 trees produced 611 kg of fruit, how many A and B trees where there.
With the former question what sort of math equation do I use for it? Ive stared myself blind on it and i dont know what the type of problem is called so i cant google it.
91.101.26.175 (talk) 19:06, 22 June 2019 (UTC)
- This is a linear Diophantine equation. Bubba73 You talkin' to me? 19:30, 22 June 2019 (UTC)
- I think I have solved the problem. I would clarify it by rewording it as follows: “An orchard contains 112 trees of two kinds - trees of kind A, and trees of kind B. One year, the average yield from kind A was about 7.7 kg per tree, the average yield from kind B was about 5.1 kg per tree, and the total yield from 112 trees was exactly 611 kg. How many trees of kind A, and how many of kind B, are there in the orchard?”
- I began by writing “let the number of trees of kind A be a, and the number of trees of kind B be b.”
- Then I wrote 7.7a + 5.1b = 611
- When eventually I solved for a and b, they were not integers, but that was because the average values of 7.7 kg per tree, and 5.1 kg per tree, were correct to two significant figures and therefore only approximations. The task becomes one of finding two integers, a and b, that yield 611 kg of fruit, bearing in mind that the average yields per tree are only approximations. Dolphin (t) 07:49, 23 June 2019 (UTC)
- Dolphin has forgotten to mention the other equation, which is a+b=112. This is a simple problem of two linear equations in two unknowns. However, solving the two equations produces the answer a = 199/13, b = 1257/13. As Dolphin says, these are not integers. But we were given the yields exactly; nothing says they were approximations. Therefore we're done: the answer is that there's no solution. Perhaps this was just a problem that the original poster made up as an example, not one that was assigned. --76.69.116.93 (talk) 08:20, 23 June 2019 (UTC)
- Dolphin forgot nothing. On the Reference Desks we don’t do people’s homework for them, but we do offer clarification or hints to help point the questioner in the right direction. The expectation is that questioners will then derive the maximum value from solving the problem for themselves.
- I agree with Bubba73 - this is a Diophantine problem: a problem whose answer must be one or more integers. In science, engineering, economics etc there are many practical problems in which the only meaningful answer is an integer. Dolphin (t) 08:28, 23 June 2019 (UTC)
- Dolphin has forgotten to mention the other equation, which is a+b=112. This is a simple problem of two linear equations in two unknowns. However, solving the two equations produces the answer a = 199/13, b = 1257/13. As Dolphin says, these are not integers. But we were given the yields exactly; nothing says they were approximations. Therefore we're done: the answer is that there's no solution. Perhaps this was just a problem that the original poster made up as an example, not one that was assigned. --76.69.116.93 (talk) 08:20, 23 June 2019 (UTC)
- Actually, I goofed up. It is a system of two linear equations. But the solutions aren't integers. A=399/26, B=2513/26. Bubba73 You talkin' to me? 03:59, 24 June 2019 (UTC)
- Regoof: "A=399/26, B=2513/26" = off-by-one twenty-sixth error. -- ToE 12:53, 25 June 2019 (UTC)
- Actually, I goofed up. It is a system of two linear equations. But the solutions aren't integers. A=399/26, B=2513/26. Bubba73 You talkin' to me? 03:59, 24 June 2019 (UTC)
The solutions are not integers if the input values were exact, which is not the case. Round the solutions to integers: A=15, B=97. Check that A+B=112. Assume that the coefficient 7.7 is exact and compute the other coefficient (611-7.7*15)/97=5.10825 which within the given precision is equal to 5.11 . Bo Jacoby (talk) 21:16, 25 June 2019 (UTC).