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.