SOLUTION: 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 ?

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 ?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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."
=
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."
=
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."
=
=
:
What is the sum of their current ages ? You can do this.
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