Help with grade 9 algebra word problem

Use an algebraic equation to solve:

Bill is twice as old as his brother Dan. In 7 years, Bill will be only one and one-half times as old as Dan. How old is Bill now?

Please explain!

Also:
Roberta is 3 years younger than Rebecca. 8 years ago, Roberta was 1/2 of Rebecca's age. How old is each girl now?

Thanks! Don't forget to explain with let statements and such!

So, you should probably start off by making an equation based on what you know. So we know Bill is twice as old as Dan, and when 7 years is added to both of their ages now that Bill will be 1.5 times as old as Dan. So:

Let x = Dan's age now, So 2x = Bill's age now

So, in 7 years:
x + 7 = Dan's age
2x + 7 = Bill's age

So using what their ages will be in 7 years, and the second sentence we are able to build our equation.
It says ''Bill will be'', meaning you put Bill's age in 7 years, then the equals sign.
Then it says ''one and a half as old as Dan'', meaning that 1.5 times Dan's age in 7 years will be after the equals sign.

So your equation should look like this:

2x + 7 = (x + 7) 1.5

Then just solve the equation:

2x + 7 = (x + 7) 1.5
2x + 7 = 1.5x + 10.5
0.5x + 7 = 10.5
0.5x = 3.5
x = 7

So, if x = 7, and Bills age NOW is 2x, Bill is 14 years old.



I hope this helps you out!! (:

the other one is:
let x = rebecca's age now
x - 3 = rebecca's age now

eight yrs ago:
(x - 3) - 8 = (1/2)(x - 8)

x - 11 = (1/2)x - 4

(1/2)x = 7

x = 14

Rebecca is 14 y.o. now
Roberta is 11 y.o. now

check -- 8 yrs ago they would be 6 and 3. that checks!

that's it! (;