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real life quadratic equations
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real life quadratic equations
chocolate problem
ball dropping
In business
Tom and Kathy together have 30 chocolates. Both of them lost 6 chocolates each, and the product of the number of chocolates now they have 80. We would like to find out how many they had to start with.
Solution:
Let the number of chocolates Tom had be x.
Then the number of chocolates Kathy had = 30 - x.
The number of chocolates left with Tom, when he lost 6 chocolates = x - 6.
The number of chocolates left with kathy, when she lost 6 chocolates
= 30 - x - 6.
= 24 - x
Therefore, their product = (x - 6) (24 - x)
= 24x - x2 - 144 + 6x
= - x2 + 30x - 144
So, - x2 + 30x - 144 = 80
- x2 + 30x - 144 - 80 = 0
- x2 + 30x - 224 = 0
x2 - 30x + 224 = 0
x(x - 16) - 14(x - 16) = 0
(x - 14)(x - 16) = 0
So, x = 14, 16
So, Tom had 14 or 16 chocolates and Kathy also had 16 or 14 chocolates
Y = P(1-2x-x^2)
P represents the cost of a Product
x represents the percentage off
Y = P(1-x)(1-x)
let P = $250 (cost of the product)
let x have two values {40%,10%}
A shoe store has a sale on designer shoes,
the original price is $250. All shoes are 40% off,
but today only you can take an additional 10% 0ff.
By using Y(the new price after deductions)
convert 40% and 10% to decimals
0.40, and 0.10
Y = $250(1-0.40)(1-0.90)
= $250(0.6)(0.90) = $135
The new price is $135
A ball is dropped from a height of 36 feet. The quadratic equation d = -t² + 36 provides the distance, d, of the ball, after t seconds. After how many seconds, does the ball hit the ground?
The ball hits the ground at d = 0. To find the value of t at this point we must solve this quadratic equation.
0 = −t² + 36
t² = 36
t = 6
(Note: t = -6 is also a solution of this equation. However, only the positive solution is valid since we are measuring seconds.)
It is common for people to add the percentages and get 50% off.
But with the equation used the percentage off is 1- (0.6)(0.9) = 46%.