the larger of two numbers is 5 less than 8 times the smaller. their sum is 94. find the numbers

smaller ---- x

larger ---- 8x - 5

solve

x + 8x-5 = 94

Let's assume the smaller number as 'x'.

According to the given information:
The larger number is 5 less than 8 times the smaller number.

So, the larger number is 8x - 5.

The sum of the two numbers is 94.

Therefore, we can write the equation as:
x + (8x - 5) = 94.

Simplifying the equation:
9x - 5 = 94.

Adding 5 to both sides of the equation:
9x = 99.

Dividing both sides by 9:
x = 11.

So, the smaller number is 11.

To find the larger number:
Substitute the value of x back into one of the equations:

Larger number = 8x - 5
Larger number = 8(11) - 5
Larger number = 88 - 5
Larger number = 83.

Therefore, the two numbers are 11 and 83.

To solve this problem, we'll use a system of equations. Let's assume that the smaller number is "x" and the larger number is "y".

We know that the larger number is 5 less than 8 times the smaller. So, our first equation is:

y = 8x - 5

We also know that the sum of these two numbers is 94. So, our second equation is:

x + y = 94

Now, we can solve this system of equations 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 + (8x - 5) = 94

Combining like terms, we get:

9x - 5 = 94

Adding 5 to both sides, we have:

9x = 99

Dividing both sides by 9, we find:

x = 11

Now we can substitute this value back into either equation to find y:

y = 8(11) - 5
y = 88 - 5
y = 83

Therefore, the smaller number is 11 and the larger number is 83.