SOLUTION: help me with this q without using substitution but by making a proper frormula and solving it. a woman is 24 years older than her daughter. two years ago she was 4 times older than
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Question 273731: help me with this q without using substitution but by making a proper frormula and solving it. a woman is 24 years older than her daughter. two years ago she was 4 times older than her daughter, find their present ages. and do this question without trial and error aswell : James has 15 times as much money as his brother. If james gives John 12 pence he then as 3 times as much as he has. how much did they each start with?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the age of the woman. Let 
represent the age of the daughter. Then:
Which can be written:
1: 
The woman's age two years ago: 
. The daughter's age two years ago: 
So we know:
)
which can be written
2: 
Now that you have two linear equations in two variables, solve the system. Multiply either equation by -1 and use the elimination method to derive a single-variable equation in . Solve for and then use that value to calculate .
***********************************************
Let represent the amount James has at the start. Let represent the amount John has at the start. Then:
Which can be written:
1: 
After James gives John 12 pence John has 
remaining, and James now has 
. Furthermore we know:
)
Which can be written:
2: 
Again, multiplying either equation by -1 sets up elimination of the variable when the equations are added. Solve for and then use that value to calculate .
John
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