Question 1036660
In 5 years the ratio of Julie's age to Song's age will be 3:5.
 In 10 years the ratio of Julie's age to Songs's age will be 2:3.
 What is the sum of their current ages?
:
let j = J's present age
let s = S's present age
:
"In 5 years the ratio of Julie's age to Song's age will be 3:5."
{{{(j+5)/(s+5)}}} = {{{3/5}}}
cross multiply
5(j+5) = 3(s+5)
5j + 25 = 3s + 15
5j = 3s + 15 - 25
5j = 3s -10
:
"In 10 years the ratio of Julie's age to Songs's age will be 2:3."
{{{(j+10)/(s+10)}}} = {{{2/3}}}
cross multiply
3(j+10) = 2(s+10)
3j + 30 = 2s + 20
3j = 2s + 20 - 30
3j = 2s - 10
:
Use elimination on these two simplified equations
Multiply the 1st equation by 2, multiply the 2nd equation by 3, we have
10j = 6s - 20
9j  = 6s - 30
--------------- subtraction eliminates s, find j
j = 10 yrs I J's present age
:
find s, using 5j = 3s - 10
5(10) = 3s - 10
50 + 10 = 3s
60 = 3s
s = 60/3
s = 20 yrs is S's present age
:
Confirm these solutions in the statement
"In 10 years the ratio of Julie's age to Songs's age will be 2:3."
{{{(10+10)/(20+10)}}} = {{{2/3}}}
{{{20/30}}} = {{{2/3}}}
:
 What is the sum of their current ages ? You can do this.