MHB Writing equation from a description

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The equation derived from the description is 2(x + y * 3 + 5 * z) = 10, indicating that "by" implies multiplication for the following terms. The discussion emphasizes the importance of interpreting the wording correctly, particularly distinguishing between "by" and "times." Participants agree that the order of operations (PEMDAS) should be applied, as there are no clear groupings provided. Simplifying the equation leads to moving constant terms to one side, but further simplification is limited without additional information. The consensus is that the initial interpretation of the equation is the most accurate.
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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.
 
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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.
 
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