Algebra 2 word problems

Question

One number is 800 less than 3 times the other, and their sum is 1,200. Find the numbers.

Which of the following equations can be used to solve the problem if the smaller number is x?

a. 2x - 800 = 1,200
b. 3x - 800 = 1,200
c. 4x - 800 = 1,200

Answer 1

Here's why I think this problem is a little tricky:

In the first sentence, they refer to "One number", and "the other(number)".

But then they ask us to right an equation where x is the smaller number.

How do we know whether x is the "One number" they talk about or "the other number"?

Well I think it's not obvious. For this reason, I think it's not a great question.

So...

I'd pick two variables other than x.

Let's use y and z.  y is "one number", and z is "the other". (This was an arbitrary choice.)

The first part of the problem says y = 3z - 800.

The second part of the problem says  y + z = 1200.

If you subtract equations, you get 0 = 4z -2000.

So z = 500, and then you can get y = 700.

So z is the smaller number, which they're calling "x".

The equation "c" is equivalent to what I wrote above: "0 = 4z -2000", but with x replacing z.

 

I think it's tempting in this problem to assume that "one number" is going to be the smaller number (x) because the statement of the problem says that it's "800 less" than something.