MHB Writing equation from a description

[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

Can someone please check this for me and tell me which way is right? I forgot how to do these type of problems.

 

[Jameson]

Re: Correct way of doing Algebra Problem

Given the way this is stated I think we can reason that "by" means to multiply everything that follows by 2, since for the other terms multiplication is written as "times". There should be a reason that they used a different word for multiplication.

For the rest of the equation we have to assume that nothing is grouped in a certain way outside of the order of operations (PEMDAS) since we have such little information.

So I agree with this interpretation you wrote:

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

You can simplify that some by getting all terms without a variable to the right side but other than that you can't do anything else.