SOLUTION: patty doesn'y feel she is really a child anymore. Ten years ago, her mother was 5 times her age. now she is 3/7 of her mother's age, and in 5 years she will be half of her mother's

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Question 95820: patty doesn'y feel she is really a child anymore. Ten years ago, her mother was 5 times her age. now she is 3/7 of her mother's age, and in 5 years she will be half of her mother's age. how old will she be when she is half her mother's age?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
m=mother's age p=patty's age
Now: m=7/3p
10 years ago: m-10=5(p-10)
m-10=5p-50
substitute 7/3p for m in the line above. 7/3p-10=5p-50
subtract 7/3p and add 50 to both sides. 40=5p-7/3p
8/3p=40
divide 8/3 into both sides. p=15 years old m=7/3*15=35 years old
When will she be 1/2 her mother's age?
2(15+x)=35+x
30+2x=35+x
subtract x and 30 from both sides. x=5 years
Check:
now: 35*3/7=15 she is 3/7 mom's age
10 years ago: p=5 m=25 mother was 5x her age.
in 5 years: p=20 m=40 she will be 1/2 mom's age.
EdJones