SOLUTION: the sum of two numbers is 26. the greater number is six more than four times the lesser number. what are the numbers?

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
RELATED QUESTIONS
the sum of a number is 27. if the lesser number is doubled, the result would be six more... (answered by lwsshak3)

The sum of two numbers is 26. The larger number is six more than four times the smaller... (answered by stanbon)

When two numbers are added together, the result is 45. Twice the greater number is six... (answered by mananth)

the sum of two numbers is 16. the greater of the two numbers is one more than four times... (answered by Fombitz)

It says to translate to an equation- The larger of two numbers is 2 more than the lesser. (answered by ankor@dixie-net.com)

the greater of two numbers is 2 more than the lesser. the sum of 25 times the greater... (answered by cathieb1225)

The lesser of two numbers is 2 less than the greater number. If 10 is subtracted from six (answered by mananth)

the greater of two numbers is 2 more than the lesser. the sum of 25 times the greater... (answered by ptaylor)

the sum of two numbers is 50. the greater number is 12 more than the lesser number. what... (answered by bucky)