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Vacation Money

Last January 2018, my family went on vacation to Cagwait White Beach Park at Cagwait, Surigao del Sur. We also celebrated the 70th birthday of our grandmother. We saved money for the said vacation. We spent 10,000 on the catering services, 5,000 on gasoline, 2,000 on room accommodation, and half of the remaining money for transportation meal. After grandmother remitted 20,000 for the income of the farm, we were left with 25,000. How much money did we save for the vacation?

Step 1. Understand the Problem

Step 2. Make a Plan

Step 3. Carry-out the Plan

Step 4. Look back on your Work/ Review your Solution.

Viole
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  • Frankly speaking, Pólya's How to Solve It is a bad book. It conditions you into thinking that there must be only one approach to solving all mathematics problems. – Parcly Taxel Nov 29 '20 at 12:54
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    @ParclyTaxel I find it isn't a bad book per se, but rather one suited for a very specific type of problem, which almost never comes up in research mathematics. Perhaps for someone who's only a beginner or is interested in mathematics as a hobby, this isn't a particularly bad approach to take. – Chubby Chef Nov 29 '20 at 12:58
  • On that note, how can one solve the problem above, and what would be the answer? Nevermind the application of Polya's steps in problem-solving. – Viole Nov 29 '20 at 13:00
  • The usual approach should work here. Declare variables for the relevant quantities which aren't specified, then write out what you are given in terms of those variables. – lulu Nov 29 '20 at 13:09
  • @Viole when you say "grandmother remitted 20,000 for the income of the farm", do you mean she added $20,000$ to the budget, or took away from it? – Chubby Chef Nov 29 '20 at 13:09
  • @ChubbyChef From what I understood, the statement "grandmother remitted 20,000 for the income of the farm" was followed up by "we were left with 25,000," which could only mean that an amount was subtracted, which would be 20,000. – Viole Nov 29 '20 at 13:15
  • To stress: to say that the grandmother "remitted" the funds is to say that she put that money into the pool, not that she was paid the money out of the pool. But this is a language issue...the math problem makes sense either way and, in both cases, it is easily solved. – lulu Nov 29 '20 at 13:34
  • @lulu The phrase "remitted 20,000 for the income" doesn't really make sense to me (had it said "from" instead of "for" the meaning would have been clear), but going off what the asker had said I interpreted it as subtraction in my answer. If the opposite meaning proves to be correct, the solution is easily fixed by changing one minus to a plus. – Chubby Chef Nov 29 '20 at 13:42
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    @ChubbyChef I agree that the phrasing is very poor, and I also note that it would be a little cold to celebrate the $70^{th}$ birthday of one's grandmother while demanding that she kick in a big block of money. As you say, both versions of the problem are easily solved. – lulu Nov 29 '20 at 14:01

1 Answers1

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We can solve this problem chronologically in the sense that we account for the information given to us in the order it arrives. First off, calculate how much money was spent in total: $$10,000+5,000+2,000=17,000.$$ We are then told that half of the remaining money was spent on transportation. Clearly, the said amount is unknown, so we declare a variable for it, say $x$. Therefore $\frac{1}{2}x$ has been spent on transportation, and $\frac{1}{2}x$ still remained. $20,000$ was then remitted to the grandmother, leaving us with $25,000$. That is, $$\frac{1}{2}x - 20,000 = 25,000.$$ This is a fairly simple equation that I trust you'll be able to solve for $x$. The only thing left to do would then be to sum up all the quantities to find out how much money we had started with.

Chubby Chef
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