SOLUTION: Maria is 15 years older than her sister Juana. Six years ago, Maria was 6 times as old as Juana. Find their present ages.

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Question 179138: Maria is 15 years older than her sister Juana. Six years ago, Maria was 6 times as old as Juana. Find their present ages.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let m = Maria's age now
let j = Juana's age now
:
write an equation for each statement:
:
"Maria is 15 years older than her sister Juana."
m = j + 15
:
" Six years ago, Maria was 6 times as old as Juana."
m - 6 = 6(j - 6)
m - 6 = 6j - 36
m = 6j - 36 + 6
m = 6j - 30
;
Find their present ages.
:
from the 1st equation, substitute (j+15) for m in the 2nd equation
j + 15 = 6j - 30
15 + 30 = 6j - j
45 = 5j
j = 45%2F5
j = 9 yrs old is Juana's age
then
9 + 15 = 24 yrs is Maria's age
:
:
Check solution in the statement:
"Six years ago, Maria was 6 times as old as Juana."
24 - 6 = 6(9 - 6)