Question

Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each?

Answer 1

The goal here is to rewrite this into an algrabra equation. Have you tried to do so? How far did you get?

Answer 2

I Tthought you had to turn it into a equation at first

Answer 3

56=8^2?

Answer 4

Actually, it is two equations. In the first part it talks about both. So if I use t for Tony and b for Belinda, it tells me:
\[t+b=56\]Now, using the same letters, you can do something like that for, "Belinda is 8 more than twice Tony’s age." Because 8 more is +8 and twice is \(2\times\).

Answer 5

What would you think the second equation would be?

Answer 6

x+(2x+8)=56
solve for x
x+2x=48
3x=48
x=16(tony)
Belinda= (2x+8)=40

Answer 7

ohhhh thanks

Answer 8

That is in one variable, which works. You may see how what I was talking about leads to that. I hope you understand the concept behind it.

Answer 9

thanks and all i ahev to do is slove for belinda right?

Answer 10

Well, if you start with \(t+b=56\), you then use the relationship between their ages to make this second equation:
\(b=2t+8\)

Then you can subsitute what you know b is into the \(t+b=56\) and get:
\(t+(2t+8)=56\)

You can see how that leads to what jillkip did?

Answer 11

So that lets you solve Tony pretty easy, then you plug Tony back into the Tony and Belinda add to 56 to find Belinda.

That is the entire process. Once you get used to it, you do shortcuts like what jillkip did and can use one variable to find both.