SOLUTION: Margaret is 16 years younger than Alice. Alice is 3 times as old as Jonathan. A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages. How old is Margaret no
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Question 333547: Margaret is 16 years younger than Alice. Alice is 3 times as old as Jonathan. A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages. How old is Margaret now? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let m = Margret's present age
let a = Alice's present age
let j = Jonathan's present age
:
Write an equation for each statement, simplify if possible:
:
"Margaret is 16 years younger than Alice."
m = (a-16)
:
" Alice is 3 times as old as Jonathan."
a = 3j
:
" A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages."
a - 1 = 2[(m-1)+(j-1)}
a - 1 = 2(m+j-2)
a - 1 = 2m + 2j - 4
a = 2m + 2j - 4 + 1
a = 2m + 2j - 3
Replace m with (a-16
a = 2(a-16) + 2j - 3
a = 2a - 32 + 2j - 3
a - 2a = 2j - 32 - 3
-a = 2j - 35
a = -2j + 35; multiplied by -1
Replace a with 3j
3j = -2j + 35
3j + 2j = 35
5j = 35
j =
j = 7 yrs, (Jon)
then
a = 3(7)
a = 21 yrs, (Alice
then
m = 21 - 16
m = 5 yrs old, is Margaret's age
:
checking this out in the statement:
" A year ago, Alice's age was twice the sum of Margret's and Jonathan's ages."
21 - 1 = 2(5 - 1 + 7 -1)
20 = 2(10), confirms our solution
:
How old is Margaret now? 5 yrs
