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and also The sum of two nubers is 90. If 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. Find the numbers.

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and also The sum of two nubers is 90. If 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. Find the numbers.

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First, let me say this is not a differential equations topic.

1.) Let

"5 times the first is three more than 6 times the second"

allows us to write:

5

The statement:

"Four times the second is five more than the first"

allows us to write:

4

I am assuming your difficulty is in setting up the equations and not is actually solving a 2X2 linear system. Can you proceed from here?

2.) Let

"The sum of two numbers is 90"

allows us to write:

The statement:

"If 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50"

If we decide to let

3

which we may arrange as:

3

Can you proceed from here?

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- Jan 26, 2012

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As MarkFL said you start with $4y = x + 5$. You're looking to get both variables on one side of the equation and the constant on the other side to match the form of your first equation. There are a couple of ways to do this, both equally valid.

$4y = x + 5$

$4y-x=5$ (1)

$4y = x + 5$

$0=x+5-4y$

$-5=x-4y$

$x-4y=-5$ (2)

(1) and (2) are really the same. If you take either one, multiply every term by -1 then you'll get the other.

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5

To eliminate

10

Now add the equations, and you will have a linear equation in

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