Question 929834
1.When Ramon was 12 years old, his father was
40.How many years must past for Ramon to be 8 years
older than one-fourth as old as his father.

let Ramon’s age {{{x}}} and father’s age {{{y}}} 
let years  be {{{n}}}



This is the overall picture

{{{Who}}}-----{{{Now}}}---{{{Future}}}
{{{Ramon}}}---{{{12}}}----{{{x}}}
{{{Father}}}---{{{40}}}---{{{y}}}	
		


So, {{{y-x=40-12}}}=>{{{y-x=28}}}......eq.1

You can get your second equation from the data.

How many years must past for Ramon to be 8 years
older than one-fourth as old as his father.

{{{12+n=(1/4)(40+n)+8}}}...........eq.2

 Solve {{{12+n=(1/4)(40+n)+8}}}

{{{12+n=10+n/4+8}}}

{{{n-n/4=10+8-12}}}

{{{3n/4=6}}}

{{{3n=24}}}

{{{n=8}}}

check:
in {{{8}}} years Ramon will be {{{12+8=20}}} and his father {{{40+8=48}}}

{{{20=(1/4)48+8}}}

{{{20=12+8}}}

{{{20=20}}}

2.The sum of the ages of Bobby and Mercy is {{{60}}}. Nine
yrs ago Bobby was twice as old as Mercy was then.Find
their present age.

let the ages of Bobby be {{{B}}} and Mercy {{{M}}}

given:

 {{{B+M=60}}} ...eq.1

Nine years ago Bobby was {{{B}}} twice as old as Mercy  {{{M}}}was then.

{{{2(B-9)=M-9}}}........eq.2

solve the system:

 {{{B+M=60}}} ...eq.1

{{{2(B-9)=M-9}}}........eq.2
______________________________

{{{B+M=60}}} ...eq.1 solve for {{{B}}}

{{{B=60-M}}} ...plug in eq.2

{{{2(60-M-9)=M-9}}}........eq.2...solve for {{{M}}}

{{{120-2M-18=M-9}}}

{{{120-18+9=2M+M}}}

{{{111=3M}}} 

{{{111/3=M}}}

{{{M=37}}}

now find {{{B}}}

{{{B=60-M}}}
{{{B=60-37}}}
{{{B=23}}}



3.Tom is {{{8}}} yrs older than Steve. Three yrs ago Steve was
{{{2}}} yrs more than one-third as old as Tom was then.
How old is Tom now?

{{{T=S+8}}} ...eq.1

{{{(1/3)(T-3)=S-3}}}........eq.2
_________________________________substitute {{{T}}} from eq.1 in eq.2

{{{(1/3)(S+8-3)=S-3}}}........eq.2.........solve for {{{S}}}

{{{(S+8-3)=(S-3)3}}}

{{{S+5=3S-9}}}

{{{9+5=3S-S}}}

{{{14=2S}}}

{{{S=7}}}

go to {{{T=S+8}}} ...eq.1 .......solve for {{{T}}}

{{{T=7+8}}} 

{{{T=15}}}