Question 1030315: The sum of two numbers is 25. The sum of the smaller and 6 times the larger is 125. Find the numbers.
Answer by mathmate(429)   (Show Source):
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Question:
The sum of two numbers is 25. The sum of the smaller and 6 times the larger is 125. Find the numbers.
Solution:
Let the two numbers be x and y, where x≤y.
In principle, this is a problem involving system of 2 linear equations, namely the system is:
x+y=25...........(1)
x+6y=125..........(2)
Subtract (1) from (2) to get
5y=100 => y=20, hence x=5.
An alternative way to solve this and similar problems is to reduce the problem to an equation of one unknown only.
Since x+y=25, we have y=25-x
For the second equation, we have x+6(25-x)=125
Simplifying,
150-125=6x-x
25=5x
x=5, hence y=20.
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