The sum of two numbers is not more than 56. One number is six times the other. Find the greatest possible values for the numbers.

x + 6x = 56

Take it from there.

5 more than -5

To find the greatest possible values for the two numbers, let's first set up the given information as equations:

Let's assume the two numbers are x and y.
According to the problem, the sum of the two numbers is not more than 56, so we can write the first equation as:
x + y ≤ 56

The second piece of information states that "One number is six times the other." In mathematical terms, we can express this as:
x = 6y

To find the greatest possible values, we need to find the highest values for x and y that satisfy both equations.

Now, we can solve this system of equations using substitution or elimination.

Substituting the value of x from the second equation into the first equation:

6y + y ≤ 56
7y ≤ 56
Dividing both sides of the inequality by 7:
y ≤ 8

Now, substituting this value of y back into the second equation to find the corresponding value of x:

x = 6y
x = 6(8)
x = 48

So, the greatest possible values for the two numbers are x = 48 and y = 8.