SOLUTION: Mary is the younger than her sister Joan. The sum of their age is 15. Twice Joan’s age is three times the sum of 5 and Mary’s age. How old are the two sisters?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Mary is the younger than her sister Joan. The sum of their age is 15. Twice Joan’s age is three times the sum of 5 and Mary’s age. How old are the two sisters?      Log On


   

Question 246125: Mary is the younger than her sister Joan. The sum of their age is 15. Twice Joan’s age is three times the sum of 5 and Mary’s age. How old are the two sisters?
Answer by marcsam823(57) About Me  (Show Source):
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Let x = Mary's age
Let y = Joan's age
Let x + y = 15
Solve for y:
y = 15 - x


Translate the words into algebra:
Twice Joan's age = 2y or 2(15-x)
3 times the sum of 5 and Mary's age = 3(5 + x)
Set these two expressions equal to each other:
2(15 - x) = 3(5 + x)
Solve:
30 - 2x = 15 + 3x
15 = 5x
x = 3
15 - x = y = 12

Mary's age is 3
Joan's age is 12
This solution also satisfies teh condition that Mary be younger than Joan