SOLUTION: Please help.The sum of three numbers is 14. The largest is 4 times the smallest, while the sum of the smallest and twice the largest is 18. Find the numbers using Cramer`s rule an

Algebra ->  Matrices-and-determiminant -> SOLUTION: Please help.The sum of three numbers is 14. The largest is 4 times the smallest, while the sum of the smallest and twice the largest is 18. Find the numbers using Cramer`s rule an      Log On


   

Question 1118003: Please help.The sum of three numbers is 14. The largest is 4 times the smallest, while the sum of the smallest and twice the largest is 18. Find the numbers using Cramer`s rule and Gaussian Elimination.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
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This problem allows a mental solution.


If x is the smallest, then the largest is 4x,  and then the condition states that


x + 2(4x) = 18,   or  9x = 18  ====>  x = 2.


Then the smallest number is 2, the largest number is 4x = 4*2 = 8,


and the middle number is the difference 14 - (2+8) = 4.


To solve it using matrix method is like shooting a cannon at sparrows.