Algebra difficulty defining equation

[late347]

Homework Statement

a memory stick was sold with 3 $ discount

seven discounted memory sticks costed 12 dollars more than five of the non-discounted-memory sticks

what is the price of non-discounted memory stick (normal price if you will)

Homework Equations

The Attempt at a Solution

This is probably simple problem to most of you guys but I always had difficulty with this type of riddles.

I don't think I ever got the reason why, why some constant value, should be added to either the left side of the equation or the right side of the equation.

x = normal price in $

x-3 = discounted price, discounted by 3$

7 * (x-3) = 5x

I'm drawing a blank here... help me out heere. Something is twelve more or twelve less. 12 needs to be added or subtracted from something I think... Reasoning is below.

But isn't the whole purpose of making an equation to say simply... the scale is now balanced.
If the scale is balanced on both sides, then the equation is balanced and the equation has some real solutions. (I think)

For inequalities, the purpose is that one side of the inequality is more than the other side.

 

[Samy_A]

Homework Statement

a memory stick was sold with 3 $ discount

seven discounted memory sticks costed 12 dollars more than five of the non-discounted-memory sticks

what is the price of non-discounted memory stick (normal price if you will)

Homework Equations

The Attempt at a Solution

This is probably simple problem to most of you guys but I always had difficulty with this type of riddles.

I don't think I ever got the reason why, why some constant value, should be added to either the left side of the equation or the right side of the equation.

x = normal price in $

x-3 = discounted price, discounted by 3$

7 * (x-3) = 5x

I'm drawing a blank here... help me out heere. Something is twelve more or twelve less. 12 needs to be added or subtracted from something I think... Reasoning is below.

But isn't the whole purpose of making an equation to say simply... the scale is now balanced.
If the scale is balanced on both sides, then the equation is balanced and the equation has some real solutions. (I think)

For inequalities, the purpose is that one side of the inequality is more than the other side.

What is more expensive: seven discounted memory sticks or five non-discounted-memory sticks?

In algebraic terms, the same question would be: which number is larger, 7 * (x-3) or 5x?

 

[late347]

What is more expensive: seven discounted memory sticks or five non-discounted-memory sticks?

In algebraic terms, the same question would be: which number is larger, 7 * (x-3) or 5x?

seven discounted sticks is more than 5 original sticks.

I think it would then be sensible and reduce the 12, from the discounted sticks.

7*(x-3) is already greater by 12, than the original 5 sticks

so it should be thus that

7*(x-3) - 12 = 5x

when the leftside gets reduced, then the both sides are the same amount. (at least it looks like so in my mind)

that one yields
7x -21 -12 = 5x
7x -33 =5x ]]]] both sides -5x

2x -33 = 0 ]]]]] both sides + 33
2x = 33

x= 33/2 dollars
x= 16,5 $

 

[Samy_A]

seven discounted sticks is more than 5 original sticks.

I think it would then be sensible and reduce the 12, from the discounted sticks.

7*(x-3) is already greater by 12, than the original 5 sticks

so it should be thus that

7*(x-3) - 12 = 5x

when the leftside gets reduced, then the both sides are the same amount. (at least it looks like so in my mind)

that one yields
7x -21 -12 = 5x
7x -33 =5x ]]]] both sides -5x

2x -33 = 0 ]]]]] both sides + 33
2x = 33

x= 33/2 dollars
x= 16,5 $

Correct.