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

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
RELATED QUESTIONS
Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago,... (answered by solver91311)

"4 years ago Jane was twice as old as Alice. In 4 more years Alice will be 2/3 of Jane's... (answered by stanbon)

Alice is twice as old as Judy, who is younger than Alex by 3 years. If the sum of their... (answered by College Student)

Tom is 15 years younger than alice. Ten years ago, Alice was 4 times as old as Tom was... (answered by Theo)

Alice is three years younger than Josh. The sum of their age is 37. How old is... (answered by josgarithmetic)

The average age of Alice and tom is 14 years 3 months. Alice is 2 years 8 months younger... (answered by lwsshak3,MathTherapy)

Practice question (Age Word Problem) The sum of the ages of Gerardo and Alice is 120... (answered by josgarithmetic)

Alice is 8 years older than bob Three years from now Alice will be twice as old as bobs... (answered by erica65404)

Marisa and Alice' age total to 44 years. If marisa is twice as old as Alice was when... (answered by ankor@dixie-net.com)