# Can you solve this simple algebra problem?

I wonder how many high school students could solve this. The answer is so simple that it seems that it should be intuitive, but I can’t solve it without doing a little bit of basic algebra.

x = 10(y-x). Solve for y in terms of (y – x).

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## 15 Answers

I could not do it in my head. I had to use simple algebra.

Loli, you are very close. Substitute for x in your equation to get y in terms of y-x.

Then I do not understand what “solve for y in terms of y-x” means.

I love the smell of Algebra in the morning. It smells like victory.

I still do not know what that means.

x=10(y-x) expresses x in terms of y-x. x is 10 times greater than the quantity (y-x). If we designate y-x as d then we can say that x =10d. There is a similar equation that gives y in terms of (y-x).

Is that what you are looking for?

x=10(y-x)

x=10y-10x

x=y+9y-10x

0=y+9y-9x

y=9y-9x

y=9(y-x)

Hang on, no, that’s wrong.

How about this:

x=10(y-x)

x=10y-10x

x=y+9y-10x

0=y+9y-11x

y=9y-11x

y=9y-9x-2x

y+2x=9(y-x)

y=9(y-x)+2x

Your original was very close: y=x/10 + x. Substitute 10(y-x) for the two x values.

Another approach starts out y= x + (y-x). Do you see how a single substitution gives us what we want?

If I substitute the x, I end up with

x=10(y-x)

10(y-x)=10(y-(10(y-x)))

y-x=y-10y-10x

y-x=-9y-10x

y=-9y-9x

y=-9(y+x)

your second one instantly resolves to y=y

y = x + (y-x) = 10(y-x) + (y-x) = 11(y-x)

From your original, y =x/10 + x = 10(y-x)/10 + 10(y-x) = 11(y-x)

I would tend to prefer to solve for y in terms of x:

x = 10(y-x)

x/10 = y – x

y = x/10 + x

y = 1.1x

But in terms of (y – x), I think it is asking us to do something like:

x = 10(y – x)

y = 10(y – x) + y – x

y = 11(y – x)

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