Question

In 3 years Dave will be 3 times as old as his brother Ray. A year ago Dave was 7 times as old as Ray. How old are the boys now?

So what i have right now for the equations are:
D + 3 = 3R
7R - 1 = D

Am i correct or at least close? Im usually not very good at these :\ and can i solve it with elimination/substitution or do i use something else?

Answer 1

Let D = Dave's age now and R = Ray's age now

Answer 2

In 3 years, Dave will be D+3 years old

Ray will be R+3 years old

Answer 3

So

"In 3 years Dave will be 3 times as old as his brother Ray"

means that

D+3 = 3*(R+3)

Answer 4

A year ago, Dave was D-1 years old. Ray was R-1 years old

So if "A year ago Dave was 7 times as old as Ray", then

D-1 = 7*(R-1)

Answer 5

okay, following so far, so i cant just use elimination on this then?

Answer 6

You can if you want, but substitution might be easier

Answer 7

D+3 = 3*(R+3)

D+3 = 3R+9

D = 3R+9-3

D = 3R+6

Answer 8

Now plug this into the second equation

D-1 = 7*(R-1)

3R+6-1 = 7*(R-1)

and solve for R

Answer 9

okay, thank you, im going to try to work it out and see if i get it right!

Answer 10

alright, tell me what you get

Answer 11

Ray is 3 so far...

Answer 12

and Dave is 15?

Answer 13

you are 100% correct

Answer 14

Yay! Thank you so much! I think i get it now :')

Answer 15

Check:

3 years from now, Dave is 15+3 = 18

3 years from now, Ray will be 3+3 = 6

Notice how Dave is 3 times as old as Ray

-----------------------------

1 year ago, Dave is 15-1 = 14

1 year ago, Ray was 3-1 = 2

and notice how Dave is 7 times as old as Ray

Answer 16

So the answer is verified

Answer 17

Thank you! You really helped me out a lot! i was really stressed over this!

Answer 18

you're welcome, I'm glad it's making sense now