SOLUTION: Banjo is twice as old as he was five years ago.His mother was then six times as old as he was then. She is now 35 years old. (a) How old is Banjo? (B) How old will Banjo be when

Question 1141469: Banjo is twice as old as he was five years ago.His mother was then six times as old as he was then. She is now 35 years old.
(a) How old is Banjo?
(B) How old will Banjo be when his mother is 50?
(c) How old was Banjos mother when he was born?
(e) What is the difference between Banjo's age and his mother's?
Found 4 solutions by Boreal, rothauserc, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Five years ago he was x, now he is 2x so x+5=2x and x=5. He is now 10.
When he was 5, his mother was 30, 35-5.
When she is 50, in 15 years, he will be 25.
She was 25 when he was born
The difference in ages is 25, since she was 25 when he was born.
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
let x be Banjos age and m be Banjos' mothers age
:
x = 2 * (x-5)
:
m = 6 * (x-5)
:
m = 35
:
(a) 35 - 5 = 6 * (x - 5)
:
30 = 6x - 30
:
6x = 60
:
x = 10
:
**********************
Banjo is 10 years old
**********************
:
(b) 50 - 35 = 15
:
10 + 15 = 25
:
**********************************************************
Banjo will be 25 years old when his mother is 50 years old
**********************************************************
:
(c) 35 - 10 = 25
:
**************************************************
Banjos' mother was 25 years old when Bano was born
**************************************************
:
(d) 35 - 10 = 25
:
****************************************
The difference in their ages is 25 years
****************************************
:

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
In this problem, the part of the formulation

"She is now 35 years old."

(in the first line) is excessive.

It follows from the first two sentences of the first line.

Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

Banjo is twice as old as he was five years ago.His mother was then six times as old as he was then. She is now 35 years old.
(a) How old is Banjo?
(B) How old will Banjo be when his mother is 50?
(c) How old was Banjos mother when he was born?
(e) What is the difference between Banjo's age and his mother's?

Let Banjo's age be B
Then we have: B = 2(B - 5)
B = 2B - 10________B - 2B = - 10______- B = - 10
a) B, or Banjo is:
b) Mom is 35, so she'll be 50 in 15 years' time, at which time Bill will
c) and e) are the same answer: Banjo's mother's age, when he was born was: , and the difference between his mother's and his age is also:
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