Question 795962: Mom here, stumped trying to help her 8th grade son in accelerated math. Help! Here is the problem-
Two sisters, Barbara and Monica, celebrate their birthday together since they were born on the same day and the same month, except that Barbara is two years younger than Monica. To a tactless question about her age, Monica replied "Barbara is very young-she is not as old as we were together 9 years ago. As for me, I am very old, because I am older than we were together nine years ago. How old is each sister?
thanks so much!!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write an equation and two inequalities for each statement, simplify as much as possible
:
"Barbara is two years younger than Monica."
b = m - 2
or
m = b + 2
:
" Barbara is very young-she is not as old as we were together 9 years ago."
b < (b-9)+(m-9)
b < b + m - 18
b + 18 < b + m
subtract b from both sides
18 < m
or
m > 18
replace m with b+2
b+2 > 18
b > 18 - 2
b > 16
:
"I am older than we were together nine years ago."
m > (b-9)+(m-9)
m > b + m - 18
m + 18 = b + m
Subtract m from both sides
18 > b
or
b < 18
Replace b with (m-2)
m-2 < 18
m < 18 + 2
m < 20
:
Look at these two statement:
b > 16. b greater than 16
and
m < 20. m less than 20
obviously since they are two years apart; b = 17 and m = 19
:
Barbara is 17, Monica is 19
:
:
You can confirm this, using these values in these two statements:
"Barbara is very young-she is not as old as we were together 9 years ago."
and
" I am older than we were together nine years ago."
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