One number is 6 less than another. If 10 times the smaller number minus 4 times the larger number is 12, find the two numbers.
y-6=x
10x-4y=12
plug first equation into second equation:
10(y-6)-4y=12
10y-60-4y=12
6y=72
y=12
12-6=x
x=6
To solve this problem, we can start by setting up two equations based on the given information.
Let's assume that the smaller number is represented by 'x' and the larger number is represented by 'y'.
From the statement "One number is 6 less than another," we can set up the equation:
x = y - 6
Now, let's use the second piece of information provided in the problem. The statement "10 times the smaller number minus 4 times the larger number is 12" can be expressed as follows:
10x - 4y = 12
We now have a system of two equations:
1) x = y - 6
2) 10x - 4y = 12
To find the values of x and y, we can solve this system of equations.
Let's solve equation (1) for x in terms of y:
x = y - 6
Now, substitute this expression for x into equation (2):
10(y - 6) - 4y = 12
Simplify the equation:
10y - 60 - 4y = 12
6y - 60 = 12
Add 60 to both sides of the equation:
6y = 72
Divide both sides of the equation by 6 to solve for y:
y = 12
Now, substitute the value of y back into equation (1) to find x:
x = 12 - 6
x = 6
Therefore, the two numbers are x = 6 and y = 12.