SOLUTION: The sum of Jane's age and Jim's age is 40. Jane's age 10 years from now will be 1 year less than 4 times Jim's age 6 years ago. Find their ages.

Question 2547: The sum of Jane's age and Jim's age is 40. Jane's age 10 years from now will be 1 year less than 4 times Jim's age 6 years ago. Find their ages.
Answer by kiru_khandelwal(79) (Show Source): You can put this solution on YOUR website!
Let Jane's age now be x and jim's age now be y
So,
x+y = 40 ...........(1)
10 yrs from now Jane's age = x+10
Jim's age 6 yrs ago = y-6
Jane's age 10 years from now will be 1 year less than 4 times Jim's age 6 years ago, so
x+10 = 4(y-6)-1 .............(2)
Now we have two equations:
x+y = 40 and x+10= 4(y-6)-1
From Ist equation :
x = 40-y..................(3)
Substituting the value of x in IInd equation:
x+10=4(y-6)-1
(40-y)+10=4(y-6)-1
40-y+10=4(y-6)-1
50-y=4y-24-1
50-y=4y-25
50+25 = 4y+y
75=5y
5y=75
y=75/5
y=15
So, Jim's age = 15
Now , x=40-y ....From (3)
So, x = 40-15 = 25
Answer,
Jane's age = 25
Jim's age = 15
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