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Question 85899: 1. Victoria's paycheck is for $x and y cents. When she cashes it the cashier accidently givese her $y and x cents. As a result Victoria has lost $95.04. HOw much was Victoria's original check for?
2. Shopko and Walmart are both offering huge saving on digital toasters. Shopko's Ad reads, "30% less than the K-Mart price". Walmart advertises, "You'd pay 35% more at K-Mart," Which store is offering the better price and by how much?
3. Shannon is the CEO of a large corporation and Emily is the president. One year the compnay makes a profit of $10,000,000 so the Board of Trustees decides to give Shannon and Emily bonuses. Shannon receives 3% of the profit after Emily's bonus is taken out and Emily receives 2% after Shannon's bonus is subtracted. How much does each woman receive (answer to the nearest whole dollar).
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Victoria's paycheck is for $x and y cents. When she cashes it the cashier accidentally gives her $y and x cents. As a result Victoria has lost $95.04. HOw much was Victoria's original check for?
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We know that the dollar amt and the cents amts will be confined to 2 digits
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Correct amt - given amt = 95.04
(x + .01y) - (y + .01x) = 95.04
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x - .01x - y + .01y = 95.04
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.99x - .99y = 95.04
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99x - 99y = 9504; multiply by 100 to get rid of the decimals.
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x - y = 96; simplified, divided equation by 99
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Because both x and y are confined to two digits, we know the value of her check has to be between 100 and 96
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we have 3, possibly 4, solutions:
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If x = 99: 99 - 96 = 3; = y = .03
Her check = 99.03 - 03.99 = 95.04
and
If x = 98: 98 - 96 = 2, y = .02
Her check = 98.02 - 02.98 - 95.04
and
If x = 97: 97 - 96 = 1; y = .01
Her check = 97.01 - 01.97 = 95.04
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I guess you call x = 96 a solution:
Her check = 96.00: 96.00 - 00.96 = 95.04
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2. Shopko and Walmart are both offering huge saving on digital toasters. Shopko's Ad reads, "30% less than the K-Mart price". Walmart advertises, "You'd pay 35% more at K-Mart," Which store is offering the better price and by how much?
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Let K-mart price = $60
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Shopko price: 60 - .3(60) = $42
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Walmart price:
Let x = Walmart price:
1.35x = 60
x = 60/1.35
x = $44.44 (Walmart price)
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3. Shannon is the CEO of a large corporation and Emily is the president. One year the company makes a profit of $10,000,000 so the Board of Trustees decides to give Shannon and Emily bonuses. Shannon receives 3% of the profit after Emily's bonus is taken out and Emily receives 2% after Shannon's bonus is subtracted. How much does each woman receive (answer to the nearest whole dollar).
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Let's do this in $1000's. S = amt of Shan's bonus and E = amt of Emil's
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S = .03(10000 - E)
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E = .02(10000 - S)
E = 200 - .02S
+.02s = 200 - E
S = 
S = (10000 - 50E); divided .02 into 10000 and 1
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Substitute for S in the 1st equation
10000 - 50E = .03(10000 - E)
10000 - 50E = 300 - .03E
10000 - 300 = +50E - .03E
9700 = 49.97E
E = 
E = 194.1164699 * 1000 = $194,117 is Emil's bonus
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Find E in terms of S and solve for S
S = .03(10000 - E)
S = 300 - .03E
+.03E = 300 - S
E = 
E = 10000 - 33.333S; divided .03 into 10000 and 1
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Substitute for E in the 2nd equation:
10000 - 33.333S = .02(10000 - S)
10000 - 33.333S = 200 - .02S
10000 - 200 = +33.333S - .02S
9800 = 33.3133S
S = 
S = 294.1768003 * 1000 = $294,177 is Shan's bonus
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Alot of chances for math errors here, check my work. Let me know if I screwed up somewhere.
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