How do you solve #w-16.7=8.27#?

1 Answer
Nov 24, 2016

#w = 24.97#


Algebraically, this is fairly easy to solve, but to have a deeper understanding of what you're trying to solve, consider this:

You have an unknown number, #w#, in which you have to remove 16.7 from it to get a known value, 8.27. To put it another way, you can think of #w# as the amount of money you gave a cashier for an item that cost $16.70, and you were given back $8.27. Since you don't know how much money you gave the cashier, you need to do a little bit of math to figure that out. What's one way you can think of approaching this problem, conceptually?

What if you just added the two amounts together? If that's what you said, than you're right!

Algebraically speaking, since you want to isolate the #w#, you will need to add 16.7 to each side. Why do you want to do that? It's because that's the only number you can add to the left side of the equation that will cause the unknown value, #w#, to be all alone.
Anything that you do to one side of the equal side, you need to do to the other.

Here's how it looks:

You started out with #w−16.7=8.27#

Adding 16.7 to each side looks like this:

#w−16.7 (+16.7)=8.27(+16.7)#

The -16.7 and the positive 16.7 cancel each other out, so now you're left with this:


Simple addition will tell you that your answer is 24.97, so:

#w = 24.97#

Something that is important to keep in mind, and that can be confusing initially, is that you can do whatever you want to one side of the equation, as long as you do it to the other side. I purposely chose to add 16.7 because I knew that it would eliminate the negative 16.7 on the left side of the equation. However, I could have added 25 (for example), as long as I did it to both sides. Adding 25, though, wouldn't be very practical because I'd be left in the same position. The idea is that you want to try to isolate the unknown variable as easily as possible.