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Math homework help!

R

RaiderJ

Diamond Member
I'm at a loss as to how to go about solving this math problem:

TWO MISSING OPERATORS
--------------------
INPUT: 8, 16
OUTPUT: 20, 40

So, 8 maps to 20, and 16 maps to 40 using two operations.

The two operations involved can be either multiplication, division, addition, or subtraction - the trick is that they have to be the same for each set of input/output.

Any idea on how to solve this, other than random guessing?


EXAMPLE:

8 (+x) || (-x) || (*x) || (%x) && (+y) || (-y) || (*y) || (%y) = 20


Problem 2 - Anyone figure this out, without guessing? (also two operations)

9 -> 58
13 -> 82
6 -> 40
 
But is there a way to figure this out WITHOUT guessing? There are other problems besides this one to figure out!
 
Originally posted by: RaiderJ
I'm at a loss as to how to go about solving this math problem:

TWO MISSING OPERATORS
--------------------
INPUT: 8, 16
OUTPUT: 20, 40

So, 8 maps to 20, and 16 maps to 40 using two operations.

The two operations involved can be either multiplication, division, addition, or subtraction - the trick is that they have to be the same for each set of input/output.

Any idea on how to solve this, other than random guessing?
Click to expand...

divide by 4 times by 10!
 
Originally posted by: RaiderJ
But is there a way to figure this out WITHOUT guessing? There are other problems besides this one to figure out!
Click to expand...

Yes, there is.

All you are doing is solving dual linear equations.


Every sequence of the four basic operations (addition, multiplication, division and subtraction) can be condensed into a single linear equation ax + b.

So in this case, we try to solve:

a * (8) + b = 20 AND
a * (16) + b = 40.

We subtract the first equation from the second to obtain

a * 16 + b - ( a * 8 + b ) = 40 - 20, or

a * 8 = 20, or a = 5/2.

We now plug a = 5/2 back into the first equation to solve for b:

(5/2) * 8 + b = 20, or
20 + b = 20, so b=0.

Hence, the series of operations for the two inputs you provided is to simply multiply them by 5/2-- which can be done in two operations (multiply by 5, then divide by 2-- or vice versa).
 
Originally posted by: MathMan
Originally posted by: RaiderJ
But is there a way to figure this out WITHOUT guessing? There are other problems besides this one to figure out!
Click to expand...

Yes, there is.

All you are doing is solving dual linear equations.


Every sequence of the four basic operations (addition, multiplication, division and subtraction) can be condensed into a single linear equation ax + b.

So in this case, we try to solve:

a * (8) + b = 20 AND
a * (16) + b = 40.

We subtract the first equation from the second to obtain

a * 16 + b - ( a * 8 + b ) = 40 - 20, or

a * 8 = 20, or a = 5/2.

We now plug a = 5/2 back into the first equation to solve for b:

(5/2) * 8 + b = 20, or
20 + b = 20, so b=0.

Hence, the series of operations for the two inputs you provided is to simply multiply them by 5/2-- which can be done in two operations (multiply by 5, then divide by 2-- or vice versa).
Click to expand...

You my friend, get a :beer:!

The sis says thanks too!
 
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