The second of two numbers is 6 times the first. Their sum is 77. Find the numbers.
6x+x = 77
7 x = 77
x = 11
6x = 66
To solve this problem, let's assign variables to the two numbers. Let's call the first number "x" and the second number "y."
According to the problem, we know that the second number is 6 times the first number. So we can write the equation:
y = 6x
We also know that the sum of the two numbers is 77. Therefore, we can write another equation:
x + y = 77
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
To do that, we can substitute the value of y from the first equation into the second equation:
x + 6x = 77
Combining like terms, we get:
7x = 77
To solve for x, divide both sides of the equation by 7:
x = 11
Now that we have found the value of x, we can substitute it back into the first equation to find y:
y = 6 * 11 = 66
Therefore, the two numbers are 11 and 66.