one number is 6 more than the other number also 7 times the smaller number is equal to 6 times the larger number find the two numbers
smaller ---- x
larger ------ x+6
7x = 6(x+6)
7x = 6x + 36
x = 36
State the conclusion
X=36
then
first number=x
=36
second number=x+6
=42
hence the two numbers are 36 and 42
Well, well, well, looks like we've got a little math puzzle here! Let's see if we can give it a comedic twist.
Let's call the smaller number "x" (because that's just how math works sometimes) and the larger number "y".
According to the information given, one number is 6 more than the other. So we have two equations to work with:
1) y = x + 6
2) 7x = 6y
Now, let's substitute equation 1 into equation 2:
7x = 6(x + 6)
Simplifying that, we get:
7x = 6x + 36
And if we subtract 6x from both sides:
x = 36
Now we can substitute the value of x back into equation 1:
y = 36 + 6
y = 42
So, the two numbers are 36 and 42. Voilà!
To solve this problem, let's break it down step-by-step.
Let's assume the smaller number is "x" and the larger number is "y".
From the given information, we can establish two equations:
Equation 1: "One number is 6 more than the other number":
y = x + 6
Equation 2: "7 times the smaller number is equal to 6 times the larger number":
7x = 6y
We now have a system of two equations with two variables. We can solve this system of equations using substitution or elimination methods.
Let's solve using the substitution method:
1. Substitute the value of y from Equation 1 into Equation 2:
7x = 6(x + 6)
2. Distribute 6 to the expression within parentheses:
7x = 6x + 36
3. Simplify the equation by subtracting 6x from both sides:
7x - 6x = 36
x = 36
4. Now substitute the value of x back into Equation 1 to find y:
y = x + 6
y = 36 + 6
y = 42
Therefore, the two numbers are 36 and 42.