F= 66
A:R = 24:8
----------------
R = 5
F:A = 63:21
-----------------
A = 30
72: 14
Ill explain how I did this later, I have to run. Got to leave for my kiddos game.
Would appreciate if anyone can help on the following question:
When F was 66 years old, the ratio of A's age to R's age was 3:1 when R was 5 yrs old, the ratio of F's age to A's age was 3:1 find the ratio of F's age to R's age when A is 30 yrs old?
So here is what I did:
I made a list assuming the 3:1 ratios did not include decimals. So I started with the first one which was A:R. You can see my chart below. Keep in mind, based on the information the problem gave you, you should have been able to easily deduce that F was the oldest and R was the youngest.
ON THE LEFT IN BROWN
I started with multiples of 3 for A that well below 66 and seemed reasonable potential ages and worked my way down. The age I input for R was simply 1/3 the age of A because there is supposed to be a 3:1 ratio between their ages at this time.
IN THE MIDDLE IN RED
The first column represents the years in time it has been compared to the first column if R is now only 5. So if you look at the first row R was 14 in the brown, so in the red he is now 5 so it has been -9 years. In other words, everyone is 9 years younger. So if R lost 9 years, that means F and A are also 9 year young so I made those calculations in the F = and A = columns.
In the first row of brown F was 66 and A was 42 so I simply subtracted 9 to get the values of 57 for F and 33 for A. When I finished that for every row I simply looked to see which pair of F and A ages had a 3:1 ratio F:A in the red columns. Once I found that I used that information for the green and final column.
ON THE RIGHT IN GREEN:
Since A is now 30 everyone is 9 years older than they were in the red column. You will notice the F = and A = in the red column that have a 3:1 ratio are bolded in black.
So we know when
R was 5
A was 21
and F was 66
So now that A is 30 it is 9 years later.
At this point I simply added 9 to F's and R's ages for a 72:14 ratio which can be reduced to -----> 36:7 ratio
let F,A,R be the ages of F,A,R today, so F=66 and A/R=3
x years ago, R was 5, so R = 5 + x
y years ago, A was 30, so A = 30 + y
x years ago, we are told that the age of F then / the age of A then was 3:1,
so (F-x) / (A-x) = 3.
solving the equations
(30+y) / (5+x) = 3 (first line)
and
(F-x)/(A-x) = 3
leads to
x=3 and y=-6 (i.e., the point when A is 30 is in the future).
Now, we would like to compute the age of F y years ago over the age of R y years ago, which would then be
(F-y)/(R-y) = (66- (-6))/(5+x-y) = 72 / 14 = 36 / 7.