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Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

solving two equation

if f(1) = 250*a = 150
f(4) = 250* a^2 = 90

solving the equation to find a

I found similar question on a book I study from an example above in the picture :

but I made my own example with simple number to make it easy to illustrate

my problem and my question is how cold he dividing the two equations ( in my example and in the book example)
what thing gives to him the mechanism to do that to find the missing "a"
I mean they are two separate equation and lets say the f(1) is mean the time in first hour, and f(4) is the time of fourth hour
so they are different so what rules he lean on it to do such thing to solve this equation by dividing the two of them by themselves

note that I create my example from the book source itself (the answer is 0.59999 which men 60% percent I know the answer for the example I made but the answer is coming out like a magic I want to understand the concept of dividing two equations togather) :

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,127

Re: solving two equation

Actually it isn't necessary to divide at all.

If 250a = 150 then a = 150/250 which is 0.6 not 0.599999999

Here's a better example where dividing helps.
ab = 10

ab^2 = 50

Because there are two letters to find we cannot solve from a single equation.

Dividing the second by the first eliminates a

b = 50/10 = 5 so a = 2

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob