SOLUTION: The sum of someone's age and her sister's age is sixty one. Twenty-three years ago, someone's was four times as old as her sister. What are the present ages of someone's age and he

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Question 176510: The sum of someone's age and her sister's age is sixty one. Twenty-three years ago, someone's was four times as old as her sister. What are the present ages of someone's age and her sister?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The sum of someone's age and her sister's age is sixty one. Twenty-three years ago, someone's was four times as old as her sister. What are the present ages of someone's age and her sister?
:
x = someone's present age
y = sister's present age
:
"The sum of someone's age and her sister's age is sixty one."
x + y = 61
or
y = (61-x)
:
"Twenty-three years ago, someone's was four times as old as her sister."
x - 23 = 4(y-23)
x - 23 = 4y - 92
x = 4y - 92 + 23
x = 4y - 69
:
What are the present ages of someone's age and her sister?
:
replace y with (61-x) using the above equation
x = 4(61-x) - 69
x = 244 - 4x - 69
x + 4x = 244 - 69
5x = 175
x = 175%2F5
x = 35 yrs someone's age
;
y = 61 - 35
y = 26 yrs sister's age
;
;
check solution in 23 yrs ago statement
35 - 23 = 4(26-23)
12 = 4(3); confirms our solution