The sum of two numbers is 9. 8 times smaller number is 2 more than 6 times the bigger number. Write an equation satisfying the statement and find the numbers
If the numbers are x and 9-x, then we have
8x = 2+6(9-x)
Now finish it off
Let's assume the smaller number as 'x' and the bigger number as 'y'.
Given:
1) The sum of two numbers is 9, which can be written as:
x + y = 9
2) 8 times the smaller number is 2 more than 6 times the bigger number, which can be written as:
8x = 6y + 2
Now we have a system of two equations:
x + y = 9 (Equation 1)
8x = 6y + 2 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Using the method of substitution:
From Equation 1, we can express y in terms of x:
y = 9 - x
Substituting this value of y in Equation 2:
8x = 6(9 - x) + 2
Simplifying the equation:
8x = 54 - 6x + 2
8x + 6x = 54 + 2
14x = 56
x = 56/14
x = 4
Now substituting the value of x back into Equation 1 to find y:
4 + y = 9
y = 9 - 4
y = 5
So the smaller number is 4 and the bigger number is 5.
To solve this problem, let's represent the two numbers with variables. Let's call the smaller number "x" and the larger number "y".
According to the statement, the sum of these two numbers is 9. So, we can write the first equation as:
x + y = 9
The second part of the statement says that 8 times the smaller number is 2 more than 6 times the bigger number. We can represent this as an equation as well:
8x = 6y + 2
Now, we have two equations representing the given information. To find the values of x and y, we can solve this system of equations.
We can use any method to solve the system, but let's use substitution.
From the first equation, we can solve for x in terms of y:
x = 9 - y
Substitute this value of x into the second equation:
8(9 - y) = 6y + 2
Now, we can solve for y:
72 - 8y = 6y + 2
Combine like terms:
72 = 14y + 2
Subtract 2 from both sides:
70 = 14y
Divide both sides by 14:
y = 5
Now, substitute this value of y back into either of the original equations. Let's use the first equation to solve for x:
x + 5 = 9
Subtract 5 from both sides:
x = 4
So, the two numbers that satisfy the given conditions are 4 and 5.