SOLUTION: Patrick's age is 20% of his mother's age. Twenty years from now, Patrick's age will be 52% of his mother's age. How old are Patrick and his mother now?
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Question 411081: Patrick's age is 20% of his mother's age. Twenty years from now, Patrick's age will be 52% of his mother's age. How old are Patrick and his mother now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let p = P's present age
Let m = Mom's present age
:
write an equation for each statement:
:
"Patrick's age is 20% of his mother's age."
p = .2m
:
"Twenty years from now, Patrick's age will be 52% of his mother's age."
p + 20 = .52(m+20)
p + 20 = .52m + 10.4
p = .52 m + 10.4 - 20
p = .52m - 9.6
replace p with .2m, from the 1st statement
.2m = .52m - 9.6
9.6 = .52m - .2m
9.6 = .32m
m =
m = 30 yrs is Mom's present age
:
Find p's age
p = .2m
p = .2(30)
p = 6 yrs is P's present age
:
:
Check this in the statement:
"Twenty years from now, Patrick's age will be 52% of his mother's age."
6 + 20 = .52(30+20)
26 = .52(50)
26 = 26; confirms our solutions
:
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