Minus' Solution to
Posted Weeks of April 20 - May 3, 1998
Minus' Solution to
If they each sell 400, Samantha makes 0.1(400)(100) = $4000
This means they sold fewer than 400 bionic kittens.
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Let's try 200. Which means Samantha makes $2000 and Tabitha makes:
They sold a little less than 200 bionic kittens.
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Let's try 180. Which means Samantha makes $1800 and Tabitha makes:
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Let's try 190. Which means Samantha makes $1900 and Tabitha makes:
If Samantha and Tabitha each sell 190 bionic kittens, they will make the same amount.
You could solve this using an algebraic formula, or by trial and error.
Let's try the trial and error method.
Tabitha makes $10 for the first ten, $20 for the second ten, $30 for the third ten. So, by the 39th ten Tabitha is making $390 (for that ten). Which means by 400 sales, Tabitha is making 39%, or: 10 + 20 + 30 + ... + 390 = 10(1 + 2 + ... + 39) = 10[39(40)/2] = $7800
10[20(21)/2] = $2100.
10[18(19)/2] = $1710.
10[19(20)/2] = $1900.
Dane Coalson and Caroline Warburton, from Pulaski Middle School, plotted out their solution like so. A nicely organized dish like this deserves recognition!
Cats Sold Samantha's Profit Tabitha's Profit 10 100 10 10 100 20 10 100 30 10 100 40 10 100 50 10 100 60 10 100 70 10 100 80 10 100 90 10 100 100 10 100 110 10 100 120 10 100 130 10 100 140 10 100 150 10 100 160 10 100 170 10 100 180 10 100 190 Totals: 190 $1900 $1900
Ben Gill, of Kent Street Senior High School in Western Australia, also choose to plot the solution out. He based his table on Tabitha's commission. Delightful!
Samantha and Tabitha each sell 190 toys and earn a commission of $1,900.% of commission # sold (for Tabitha) commission paid total earnings 10 1% $10 $10 20 2% $20 $30 30 3% $30 $60 40 4% $40 $100 50 5% $50 $150 ~ ~ ~ ~ 100 10% $100 $550 110 11% $110 $660 120 12% $120 $780 130 13% $130 $910 140 14% $140 $1050 150 15% $150 $1200 160 16% $160 $1360 170 17% $170 $1530 180 18% $180 $1710 190 19% $190 $1900 If Samantha sells 190 toys at 10% commission she makes 10% of $19,000 which is also = $1,900. Therefore, they sell 190 toys each.
The following chefs also provided Minus with solutions. Most of which were tables, and a few were just plain answers. No one provided us with the correct algebraic formula. Aww...that's okay. Minus only likes the fresh stuff anyways... Yuk! Yuk!
Verni Sundararajan [verni@hotmail.com]Eloise Fardon of St. Hilda's in Western Australia
Dave A.K.A: I-Wanna-Harder-Challenge Man [mckechnied@cses.scbe.on.ca]
Kamala Gracie of St Hilda's in Western Australia
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