Quadratic equations: Give me a WORD problem, then show me the equation...?

Question

I want to know what these things are used for and how to use them.  Give me a simple word PROBLEM and the solution.

I asked this before, so let me be absolutely clear this time:
I have two apples, I give one away, therefore I now have one apple: 2-1=1 
THAT'S a word problem and the equation.

"A hundred years ago, half the population died in birth and the other half died at sixty.  60+0=60/2= average age of 30." - THAT is ALSO a word problem.

What I'm not looking for is "My favorite application is something called the golden ratio; a special ratio that is used in all sorts of architecture and can be found in nature; the most classic example is the nautilus shell. In order to get the golden ratio, you use a quadratic formula:

x^2 - x = 1
x^2 - x - 1 = 0
x = [(5)^1/2 -1] / 2 = 1.61803399" - that's an example, but it's not a WORD PROBLEM - it doesn't SOLVE anything for me.

No - the teachers aren't telling us this.
No - the teachers don't KNOW why or how they're used.
YES - I DID ask.
No - they said the only reason we learned them is because they're on the test.

I'm an adult now, and I'd like to know what the Hell is going on here!

Joshua L · Accepted Answer

A 100 m length of steel cable is threaded through a series of posts in order to construct a fence around a paddock with four straight sides.
a) Write an equation which links l and w.
b) Rearrange the equation in part a to write an expression for l in terms of w.
c) Write an expression for the area of the paddock in terms of w.
d) What is the maximum area of the paddock?
e) What values of l and w give the maximum area of the paddock?
f) Comment on the relationship between l and w, hence stating what type of shape the paddock is.

Answers:
a) 100 = 2l + 2w

b) 2l = 100 − 2w
l = 50 − w

c) Area = l × w
= (50 − w) w
= 50w − w^2

d) Max area = 625 metres squared
this can be seen on a graph where the maximum height of the graph is.

e) w = 25 m
l = 50 − w
l = 50 − 25
l = 25 m

f) The paddock is a rectangle measuring 25 m × 25 m, hence it is a square.

Shirley · Answer

The height is h The base is 8h If we double both, we get 2h and 16h The are of a parallelogram is b * h, so the area of the new larger one is 2h * 16h = 32h^2 The area of the old smaller one is b * h = 8h * h = 8h^2 32h^2 - h^2 = 384 24h^2 = 384 h^2 = 16 h = 4 So the original parallelogram had a height of 4 and a base of 32.

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Quadratic equations: Give me a WORD problem, then show me the equation...?

2 Answers