SOLUTION: I have to put this in augmented matrix form, then I can solve. I need help finding variables.
The average age of the Smith's cars is eight years. Three years ago the Toyota wa
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-> SOLUTION: I have to put this in augmented matrix form, then I can solve. I need help finding variables.
The average age of the Smith's cars is eight years. Three years ago the Toyota wa
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Question 31736: I have to put this in augmented matrix form, then I can solve. I need help finding variables.
The average age of the Smith's cars is eight years. Three years ago the Toyota was twice as old as the Ford. Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota. How old is each car now?
x - toyota
y - ford
z - buick
x + y + z/3 = 8 (..or x+y+z = 24 ?)
in 2003 x = 2y (...or x - 3 = 2y -3
in 2004 y + z = z (...or (y+z)-2 = z
- am I on the right track ????
thanks in advance
Jane
You can put this solution on YOUR website! Hello!
You appear to be in the right track. These are the three equations that can be deduced from teh data in the problem:
"The average age of the Smith's cars is eight years" , or (you got this one right)
"Three years ago the Toyota was twice as old as the Ford"
This means that the current age of the toyota minus 3, is twice as much as the current age of the Ford minus 3. So we get the equation:
Let's put it in aX + bY + cZ = D form, so then it's easy to write it as a matrix. The above equation implies that:
Finally,
"Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota"
Using the same reasoning as in the previous equation, this statement implies that:
Let's put it in the same form:
Therefore, written in matrix form, this problem becomes:
(