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Question 922670: the sum of two numbers is 26. the greater number is six more than four times the lesser number. what are the numbers?
Answer by drvidmar(5)   (Show Source):
You can put this solution on YOUR website! the sum of two numbers is 26. the greater number is six more than four times the lesser number. what are the numbers?
Answer:
Let's call the unknown numbers n and m. Let n be the bigger one.
The first sentence we can express by the equation
n + m = 26
The second sentence is a little more complicated, but can be expressed as follows:
n = 4m + 6
Now, we have two equations expressing n in terms of m. The second is the simplest to start with because n is already isolated on one side of the equation. So we use that expression for n in the first equation and get an equation with only one variable and some numbers in it, which is what we are always aiming for when solving simultaneous equations.
So, putting the expression for n from the second equation into the first equation, we get:
(4m+6) + m = 26
simplifying,
4m + 6 + m = 26
combining the terms using m,
5m +6 =26
getting rid of the 6 on he left side by subtracting 6 from both sides of the equation, we get
5m = 20
Since 5 times m is 20, m is 4.
Now, to go back and get n, we use the first equation,
n + m = 26
Substituting the value of m into the equation we get
n + 4 = 26
subtracting 4 from both sides to isolate n, we get
n = 22.
So our answer is m = 4 and n = 22
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