# Riddle me this. Help! **URL:** \ **Category:** Factual Questions\ **Created:** [May 24, 2003, 8:45pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281 "2003-05-24T20:45:38Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Fugazi79](https://avatars.discourse-cdn.com/v4/letter/f/ccd318/32.png) [@Fugazi79](https://boards.straightdope.com/u/Fugazi79)\ **Post date:** [May 24, 2003, 8:45pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/1 "2003-05-24T20:45:38Z")
The Pharaoh’s cook has made three trips to the market. On each trip he made, he bought a different combination of fruit, and paid the number of coins shown below. The price of each fruit did not change. What is the total cost of an apple, an orange, and a pear? [http://www.puzzleadventure.com/puzzles/ffrolics.gif](http://www.puzzleadventure.com/puzzles/ffrolics.gif) ---
**Author:** ![lord\_vykor](https://avatars.discourse-cdn.com/v4/letter/l/e495f1/32.png) [@lord\_vykor](https://boards.straightdope.com/u/lord_vykor)\ **Post date:** [May 24, 2003, 9:03pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/2 "2003-05-24T21:03:47Z")
Looks like a straightforward algebra problem to me (maybe I’m just not getting the “riddle”). Since the cost of each fruit does not change, a system of equations could do this… Assume x is cost of apples in coins, y is cost of oranges, z is cost of pears. Given the diagram then 3x + 4y + 5z = 97 coins 5x + 3y + 4z = 89 coins 4x + 5y + 3z = 90 coins Solving for x, y, and z should get x = 5, y = 8, z = 10 So one apple costs 5 coins, one orange cost 8 coins, and one pear costs 10 coins. Did I miss the point of the riddle? ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [May 24, 2003, 9:04pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/3 "2003-05-24T21:04:06Z")
It’s a system of equations. I’ll give you a hint to help you solve it on your own, if you’d like: Write it out like this: 3x + 4y + 5z = 97 5x + 3y + 4z = 89 4x + 5y + 3z = 90 Then use any of several algebraic methods for solving systems of equations (use Google of you can’t remember high school algebra ;)) to solve for x, y and z. Good luck! ---
**Author:** ![Daydreamer](https://avatars.discourse-cdn.com/v4/letter/d/e9a140/32.png) [@Daydreamer](https://boards.straightdope.com/u/Daydreamer)\ **Post date:** [May 24, 2003, 9:27pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/4 "2003-05-24T21:27:35Z")
Or if you dislike multiple-equation algebra as much as I do, you can solve for one variable (generally z), and graph the three on a graphing calculator. These three lines, if done properly, will cross at (5,8,10) - who would have thunk it? 🙂 ---
**Author:** ![USCDiver](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/uscdiver/32/354_2.png) [@USCDiver](https://boards.straightdope.com/u/USCDiver)\ **Post date:** [May 24, 2003, 9:55pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/5 "2003-05-24T21:55:51Z")
Do we know that all the coins are worth the same amount? Could be combinations of quarters, dimes and nickels. Of course this would make the problem impossible. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [May 24, 2003, 10:14pm UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/6 "2003-05-24T22:14:03Z")
> [@](#): > > \*Originally posted by Daydreamer \* > \*\*Or if you dislike multiple-equation algebra as much as I do, you can solve for one variable (generally z), and graph the three on a graphing calculator. These three lines, if done properly, will cross at (5,8,10) - who would have thunk it? 🙂 \*\* My Casio 985o-Ga Plus will solve them through direct-entry. Of my 8 scientific calculators, this is perhaps my favorite. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [May 25, 2003, 12:53am UTC](https://boards.straightdope.com/t/riddle-me-this-help/177281/7 "2003-05-25T00:53:04Z")
> [@](#): > > \*Originally posted by USCDiver \* > \*\*Do we know that all the coins are worth the same amount? Could be combinations of quarters, dimes and nickels. Of course this would make the problem impossible. \*\* Pssst! The hero of the “riddle” was a _pharaoh’s cook_ – the dollar wasn’t about to become popular for \ millenia.