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# Solving Puzzle using Maths

• 18-01-2013 6:32pm
Registered Users Posts: 291 ✭✭

Trying to solve these kind of puzzles that appear in the Daily Mail.

"Emily sold a phone to Josephine for 30 per cent more than she paid for it. Josephine made a £50 loss when she sold it to Sophie, who made a 15 per cent loss when selling it to Kelly. If Kelly paid £289 for the phone, how much did Emily pay for it?"

Can remember them from Leaving Cert Maths classes expressing them as x,y and z and playing them off each but havent a clue how to do them anymore.
Anyone any ideas?

• Registered Users Posts: 338 ✭✭

You'd be more likely to get help on the maths forum!

http://www.boards.ie/vbulletin/forumdisplay.php?f=380

• Registered Users Posts: 6,344 ✭✭✭

The trickiest bit for me was the 15% loss.

I started from the bottom up.

Kelly paid £289 (which was a 15% loss for Sophie)

So Sophie paid 289/0.85 = £340. The 15% loss means Sophie sold it for 85% (0.85) of what she sold it for. SophieBuyPrice * 0.85 = KellyBuyPrice. Given that we know KellyBuyPrice, we divide that by 0.85, giving us £340.
Sophie bought it for £340, which was a £50 loss for Josephine, so Josephine paid £390.

Emily sold it to Josephine for a 30% profit (130% = 1.3). So Emily paid £390/1.3 = £300

If you take the letters of the girls' names as the variables (E, J, S and K), then the formula is

K = 289; S= K/0.85; J = S +50; E = J/1.3
==>
((K/0.85)+50)/1.3 = E