Can someone please check this algebra problem?

[Joystar77]

The result of multiplying 2 by x plus y times 3 plus 5 times z is equal to 10.

2x + y * 3 + 5 * z = 10

2x + 3y + 5z = 10

or

2 (x + y * 3 + 5 * z) = 10

2x + 2y + 6 + 10 + 2z = 10

2x + 2y + 16 + 2z = 10

I forgot how to do these type of problems of translating algebraic verbal expressions. Can someone please check this and tell me which way is right? If not, can you explain this and correct it for me?

 

[Romsek]

The result of multiplying 2 by x plus y times 3 plus 5 times z is equal to 10.

2x + y * 3 + 5 * z = 10

2x + 3y + 5z = 10

This is fine

or

2 (x + y * 3 + 5 * z) = 10

This step is incorrect and so is the rest of what you have written




2x + 3y + 5z = 10 is pretty much as far as you can simplify this without more information

 

[Romsek]

NO!

y * 3 is same as 3y, 5 * z same as 5z

2(x + 3y + 5z) = 10
2x + 6y + 10z = 10
You can divide by 2 to simplify:
x + 3y + 5z = 5

What grade are you in?

The original language is pretty ambiguous.

The result of multiplying 2 by x plus y times 3 plus 5 times z is equal to 10.

does this mean

2*(x + 3y + 5z) = 10

or

2x + 3y + 5z = 10

or maybe even

2*(x + y)(3 + 5z) = 10

it's pretty impossible to tell from the wording. You chose the first interpretation, I chose the second.

Issues like this is why mathematical notation exists.

 

[Joystar77]

Thanks Romsek for checking this problem for me.

This is fine



This step is incorrect and so is the rest of what you have written




2x + 3y + 5z = 10 is pretty much as far as you can simplify this without more information

 

[Joystar77]

Denis, don't be making fun of me just because I forgot how to translate a verbal algebraic expression. At least, I gave it a try and showed my work.

NO!

y * 3 is same as 3y, 5 * z same as 5z

2(x + 3y + 5z) = 10
2x + 6y + 10z = 10
You can divide by 2 to simplify:
x + 3y + 5z = 5

What grade are you in?

 

[Joystar77]

Thank you Romsek for explaining this to me and I do realize that using mathematical notation is of utmost importance.

The original language is pretty ambiguous.

The result of multiplying 2 by x plus y times 3 plus 5 times z is equal to 10.

does this mean

2*(x + 3y + 5z) = 10

or

2x + 3y + 5z = 10

or maybe even

2*(x + y)(3 + 5z) = 10

it's pretty impossible to tell from the wording. You chose the first interpretation, I chose the second.

Issues like this is why mathematical notation exists.