The larger of two numbers is 2 more than 3 times the smaller. If the sum of the numbers is 34, find the smaller number.
x+y = 34
x = 3y+2
y=8
Let's call the smaller number "x" and the larger number "y".
According to the given information, we can write two equations:
1. "The larger of two numbers is 2 more than 3 times the smaller":
y = 3x + 2
2. "The sum of the numbers is 34":
x + y = 34
Now we can solve these equations simultaneously to find the value of the smaller number "x".
Let's substitute the value of "y" from equation 1 into equation 2:
x + (3x + 2) = 34
Now, simplify the equation:
4x + 2 = 34
Subtract 2 from both sides of the equation:
4x = 32
Divide both sides of the equation by 4:
x = 8
Therefore, the smaller number is 8.
To solve this problem, let's create two variables to represent the numbers: let's call the larger number L and the smaller number S.
We can translate the first sentence into an equation: "The larger of two numbers is 2 more than 3 times the smaller." This can be written as:
L = 3S + 2
The second sentence tells us that the sum of the numbers is 34. This can also be written as an equation:
L + S = 34
Now we have a system of two equations:
L = 3S + 2
L + S = 34
To solve this system, we'll use the method of substitution.
We can substitute the value of L from the first equation into the second equation:
(3S + 2) + S = 34
Simplifying this equation:
4S + 2 = 34
Next, we can isolate the variable S by subtracting 2 from both sides of the equation:
4S = 34 - 2
4S = 32
Finally, we divide both sides of the equation by 4 to solve for S:
S = 32/4
S = 8
Therefore, the smaller number is 8.