SOLUTION: The sum of two numbers is 31. Twice the lesser number is 6 less than twice the greater number. What are the numbers?

Question 94894: The sum of two numbers is 31. Twice the lesser number is 6 less than twice the greater number. What are the numbers?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let L represent the lesser number and G represent the Greater.
.
The sum of these two numbers equals 31. In equation form this is:
.
L + G = 31 <=== remember this first equation
.
Twice the lesser number (L) plus 6 equals twice the greater number (G). In equation form
this is:
.
2L + 6 = 2G <=== this is the second equation
.
From the first equation we can solve for L by subtracting G from both sides. When you subtract
G from both sides of the first equation the result is given by:
.
L = 31 - G
.
In the second equation you can substitute 31 - G in place of L. The second equation then
becomes:
.
2(31 - G) + 6 = 2G
.
Do the distributed multiplication on the left side by multiplying 2 times 31 and 2 times -G
to get:
.
62 - 2G + 6 = 2G
.
Get rid of the -2G on the left side by adding 2G to both sides. When you do that the equation
becomes:
.
62 + 6 = 4G
.
Add the two numbers on the left side:
.
68 = 4G
.
Solve for G by dividing both sides of this equation by 4 (the multiplier of G) and get:
.
68/4 = G
.
Dividing 68 by 4 results in 17 and the equation is then:
.
G = 17
.
We now know that the greater number is 17, and since the two numbers add to 31, the lesser
number L must be 31 - 17 = 14.
.
So the two numbers are 17 and 14
.
Check: twice the lesser number is 2 times 14 or 28. Is this 6 less than twice the greater
number or 2 times 17 = 34. Yes, 28 is 6 less than 34. Our answers check. The two numbers are
14 and 17.
.
Hope this helps you to understand the problem.

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