Solve T = x + y + z, z = 5000, y = 15000, x = 0.60 * T for T

[Savrot]

Hi! I need help to understand how to solve this. In the book, it says that the information provided is enough since the number of unknown variables are equal to the number of independent equations.

Find out what T is

T = x + y + z
z = 5000
y = 15000
x = 0.60 * T

So the answer is that t = 50'000 but i do not understand how to get there.

independent equationsindependent equationsofindependent equations

 

[tkhunny]

" the number of unknown variables are equal to the number of independent equations. "

This is good, but the most important word in there is "independent". It is NOT a good rule of thumb without that word.

Have you considered direct substitution?

T = x + y + z
z = 5000
y = 15000
x = 0.60 * T

T = (0.60 * T) + 15000 + 5000

 

[stapel]

Hi! I need help to understand how to solve this. In the book, it says that the information provided is enough since the number of unknown variables are equal to the number of independent equations.

Find out what T is

T = x + y + z
z = 5000
y = 15000
x = 0.60 * T

So the answer is that t = 50'000 but i do not understand how to get there.

Since there is no "t" in what you've posted, it is impossible "to get there"! Did you perhaps mean that "T = 50,000"? If so, then what methods has your class covered for solving systems of equations? For instance, you plugged the given values and one expression from the second through fourth equations in place of the variables on the right-hand side of the first equation, and... then what?

Please be complete. Thank you!

 

[Savrot]

" the number of unknown variables are equal to the number of independent equations. "

This is good, but the most important word in there is "independent". It is NOT a good rule of thumb without that word.

Have you considered direct substitution?

T = x + y + z
z = 5000
y = 15000
x = 0.60 * T

T = (0.60 * T) + 15000 + 5000

Hm i might be unclear what independent mean. What it says in my book is that "an independent equation is an equation that cannot be written to be the same"


I am sorry, i do not know what direct subsitution is.

 

[Savrot]

Since there is no "t" in what you've posted, it is impossible "to get there"! Did you perhaps mean that "T = 50,000"? If so, then what methods has your class covered for solving systems of equations?
Please be complete. Thank you!

No there actually is no T so i'm thinking that it might be an typo.

Im not actually in a class. I'm doing something that is called "högskoleprovet" in sweden. It's a test that if you score high on it you can educate yourself to whatever you want (since school is free here). It's completely broken since you only need to get good on the things that is covered in the test which is basic math, swedish and english. So i'm learning the math that i need to get good on this test which is very specific.

For instance, you plugged the given values and one expression from the second through fourth equations in place of the variables on the right-hand side of the first equation, and... then what?

Yeah that's what i thought aswell! But in the book it just said "Since you have 4 unkown variables and 4 independent equation you can solve this"

 

[stapel]

...For instance, you plugged the given values and one expression from the second through fourth equations in place of the variables on the right-hand side of the first equation, and... then what?

Yeah that's what i thought aswell! But in the book it just said "Since you have 4 unkown variables and 4 independent equation you can solve this"

I'm not understanding your statement, "Yeah that's what i thought aswell". I asked you what you got when you followed the simplest solution process, and the book agrees that this is solvable. Why are you thinking that it is not solvable?

Meanwhile, my question stands. After you plugged the given values and expression in for the variables in the given equation, what did you get? Where did this lead?

Please show your work. Thank you!

 

[Savrot]

I'm not understanding your statement, "Yeah that's what i thought aswell". I asked you what you got when you followed the simplest solution process, and the book agrees that this is solvable. Why are you thinking that it is not solvable?

Meanwhile, my question stands. After you plugged the given values and expression in for the variables in the given equation, what did you get? Where did this lead?

Please show your work. Thank you!

I'm sorry, i did not properly understand what you were saying.

T = 0,60 * T + 15000 + 5000

This is as far as i come, because 0,60 of the total amount might be anything and i do not how the book comes up with the solution that T = 50'000, since this information is not given.

We know that x is 60% of T, but i do not understand how this helps me to specify what T is. The Z and Y variables do not seem to help since 20000 + T might still become anything.

Am i completely of off on this?

 

[Deleted member 4993]

I'm sorry, i did not properly understand what you were saying.

T = 0,60 * T + 15000 + 5000 .................................................(1)

This is as far as i come, because 0,60 of the total amount might be anything and i do not how the book comes up with the solution that T = 50'000, since this information is not given.

We know that x is 60% of T, but i do not understand how this helps me to specify what T is. The Z and Y variables do not seem to help since 20000 + T might still become anything.

Am i completely of off on this?

Using (1):

T = 0,60 * T + 15000 + 5000

T - 0,60 * T = 15000 + 5000

continue....

 

[Savrot]

Using (1):

T = 0,60 * T + 15000 + 5000

T - 0,60 * T = 15000 + 5000

continue....

Oh i think i get it now.

T - 0,60 * T = 20'000

Now all you need to do is to figure out what number would have to be multiplied by 0,6 so that removing the sum would leave 20'000.

So it would be:

50'000 - 0,60 * 50'000 = 20'000

Now i knew that T was 50'000. What would be a smart way to find this out without knowing it?

 

[Savrot]

Oh i think i get it now.

T - 0,60 * T = 20'000

Now all you need to do is to figure out what number would have to be multiplied by 0,6 so that removing the sum would leave 20'000.

So it would be:

50'000 - 0,60 * 50'000 = 20'000

Now i knew that T was 50'000. What would be a smart way to find this out without knowing it?

Oh wait, i just divided 20'000/0,4 = 50000

 

[Savrot]

Can you solve this for x:
x - .3x = 14

Yes i finally figured this out.

x - 0,3x = 14

14/0,7 = 20

20 * 0,3 = 6

20 - 6 = 14

Is this line of thinking correct ?

 

[Savrot]

Correct, but your teacher may insist you
show more "stuff", like:
x = 14/0,7
x = 20

Google "solving equations with 1 unknown".

Thank you Denis! And thanks to everybody else for the help! What a great forum this is

 

[stapel]

T - 0,60 * T = 20'000

Now all you need to do is to figure out what number would have to be multiplied by 0,6 so that removing the sum would leave 20'000.

So it would be:

50'000 - 0,60 * 50'000 = 20'000

Now i knew that T was 50'000. What would be a smart way to find this out without knowing it?

To learn how to solve linear equations, try here.