SOLUTION: The sum of two numbers is 17. The second number is 2 more than twice the first number. Find the two numbers.

Algebra ->  Expressions-with-variables -> SOLUTION: The sum of two numbers is 17. The second number is 2 more than twice the first number. Find the two numbers.      Log On


   

Question 100844: The sum of two numbers is 17. The second number is 2 more than twice the first number. Find the two numbers.
Found 2 solutions by doukungfoo, bucky:
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
Lets call the first number x
now define the second number in terms of x
Given: The second number is two more than twice the first
2x+2
Given: the sum of two numbers is 17
write an equation
(x)+(2x+2)=17
solve for x
x+2x+2=17
3x+2=17
3x=15
x=5
Answer: first number is 5
solve for second number
2x+2=second number
2(5)+2=second number
10+2=12
Answer: second number is 12
check
12+5=17

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The problem asks you to find two unknown numbers. So let's start by calling one number x and
the other number y.
.
The problem tells you that if you add the two numbers, the sum is 17. In equation form this
can be written as:
.
x + y = 17 <=== call this equation 1
.
The problem then tells you that the second number (call it y) is 2 more than twice the other
number. That means it equals 2 more than 2x. So in equation form you can write:
.
y = 2x + 2 <=== call this equation 2
.
Return to equation 1. If you subtract x from both sides of this equation you change that
equation to y = 17 - x. Since we now know that y equals 17 - x we can replace y by 17 - x
in equation 2 to get:
.
17 - x = 2x + 2
.
Let's collect the x terms on the left side of this equation and the numbers on the right side
of the equation. Start by getting rid of the 17 on the left side by subtracting 17 from both
sides to get:
.
-x = 2x -15
.
Then get rid of the 2x on the right side by subtracting 2x from both sides to get:
.
-3x = -15
.
Now you can solve for x by dividing both sides of this equation by -3. When you do that
division the result is:
.
x = -15/-3 = 5
.
So one of the numbers is 5. And since the two numbers total 17, the other number must be
17 - 5 = 12.
.
As a quick check, you can double the smaller number and add 2. In other words, 2 times 5
equals 10 and add 2 to get 12. That equals the second number, so our answer is correct.
.
The two numbers you were asked to find are 5 and 12.
.
Hope this helps you to understand the problem.
.