Question

Two positive numbers have a difference of 18. The larger number is 2 less than 6 times the smaller number. What are the numbers?

Answer 1

First number is 4 and second is 22

Explanation:

Let's call the smaller number "x" and the larger number "y." According to the information given:

1. The difference between the two numbers is 18:

y - x = 18

2. The larger number is 2 less than 6 times the smaller number:

y = 6x - 2

Now, we can solve this system of equations. First, let's use equation 1 to express "y" in terms of "x":

y = 18 + x

Now, we can substitute this expression for "y" into equation 2:

18 + x = 6x - 2

Now, let's solve for "x" by rearranging the terms:

18 + 2 = 6x - x

20 = 5x

Now, divide both sides by 5 to find the value of "x":

x = 20/5

x = 4

Now that we have the value of "x," we can find "y" using the expression we found earlier:

y = 18 + x

y = 18 + 4

y = 22

So, the two numbers are x = 4 and y = 22.