The larger of two numbers is one more than four times the smaller number. If the sun of the numbers is 106 find the numbers, show steps
Let's assume the smaller number is x.
So, the larger number is 4x+1.
Since the sum of the numbers is 106, we can write the equation as: x + 4x + 1 = 106.
Combining like terms, we have: 5x + 1 = 106.
Subtracting 1 from both sides of the equation, we get: 5x = 105.
Dividing both sides by 5, we obtain: x = 21.
Therefore, the smaller number is 21.
Substituting the value of x into the equation for the larger number, we have: 4(21) + 1 = 84 + 1 = 85.
Hence, the larger number is 85.
Let's assume the two numbers as x and y, where x is the larger number.
According to the given information:
x = 4y + 1 -- (Equation 1)
x + y = 106 -- (Equation 2)
Now we can solve the system of equations by substitution or elimination method.
Substitution method:
From Equation 1, we can express x in terms of y:
x = 4y + 1
Substituting x = 4y + 1 into Equation 2, we get:
(4y + 1) + y = 106
Combining like terms:
5y + 1 = 106
Subtracting 1 from both sides:
5y = 105
Dividing by 5:
y = 21
Substituting the value of y back into Equation 1, we can find x:
x = 4(21) + 1
x = 85
Therefore, the two numbers are 85 and 21.
Let's assume the smaller number as 'x' and the larger number as 'y'.
From the given information, we can form two equations:
1. The larger number is one more than four times the smaller number:
y = 4x + 1
2. The sum of the numbers is 106:
x + y = 106
To solve this system of equations, we'll substitute the value of 'y' from equation 1 into equation 2:
x + (4x + 1) = 106
Simplifying the equation:
5x + 1 = 106
Subtracting 1 from both sides:
5x = 105
Dividing both sides by 5:
x = 21
Now, substitute the value of 'x' back into equation 1 to find 'y':
y = 4(21) + 1
y = 84 + 1
y = 85
Therefore, the two numbers are 21 and 85.