Question 87029: Q1: Three years ago, Mark's age was 1 year more than thrice Aaron's. Four years from now, Mark's age will be 2 years more than twice Aaron's. How old is Mark?
Q2: Mike's father is twice as old as he is. Seven years ago, the father was 7 years less than thrice the old of Mike was. Find Mike's present age?
Q3: Seven years ago, Mary was 6 times as old as Cora. In one year, she will be only twice as old as Cora. Find their present ages?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q1: Three years ago, Mark's age was 1 year more than thrice Aaron's. Four years from now, Mark's age will be 2 years more than twice Aaron's. How old is Mark?
--------------------------------
Let Aaron's age NOW be "x"
Three years ago DATA:
Aaron's age = x-3 ; Mark's age = 3(x-3)+1= 3x-8
-------------
Four years from Now DATA:
Note: Four years from not is seven years after three years ago:
Aaron's age = x+4 ; Mark's age = 3x-8+7 = 3x-1
---------------
EQUATION
Using Four years from now DATA:
Mark = 2*Aaron+2
3x-1 = 2*(x+4)+2
3x-1 = 2x+10
x=11 (Aaron's age NOW)
--------
Three years ago Mark was 3x-8 = 3*11-8 = 25
Mark is NOW 25
===================
Q2: Mike's father is twice as old as he is. Seven years ago, the father was 7 years less than thrice the old of Mike was. Find Mike's present age?
----------
NOW DATA:
Mike's age = x ; Father's age = 2x
------------------
Seven Years Ago DATA:
Mike age = x-7 ; Father's age = 2x-7
------------------
EQUATION:
Father's age = 3*Mike -7
2x-7 = 3(x-7)-7
2x-7 = 3x-21-7
2x-7 = 3x-28
x = 21 (Mike's age NOW)
-----------------------
Q3: Seven years ago, Mary was 6 times as old as Cora. In one year, she will be only twice as old as Cora. Find their present ages?
--------------
Let Cora's age NOW be "x".
---------
Seven Year ago DATA:
Cora's age was x-7 ; Mary was 6(x-7) = 6x-42
-------
This implies that Mary's age NOW is 6x-42+7 = 6x-35
========
One year from now DATA:
Cora = x+1 ; Mary = 6x-35+1 = 6x-34
----------------
EQUATION:
In one year Mary will be twice as old as Cora:
6x-34 = 2(x+1)
6x-34 = 2x+2
4x = 36
x = 9 (Cora's age NOW)
6x-35 = 6*9-35 = 19 (Mary's age NOW)
===============
Cheers,
Stan H.
|
|
|
