The difference between two numbers 19.5. The larger number is 11 times as much as the smaller number. Find the larger number.
Let's call the smaller number x and the larger number y.
According to the problem, the difference between the two numbers is 19.5, so we can write the equation:
y - x = 19.5
We also know that the larger number is 11 times as much as the smaller number, so we can write the equation:
y = 11x
Now we can substitute the second equation into the first equation to solve for x:
11x - x = 19.5
10x = 19.5
x = 1.95
To find the larger number, we substitute the value of x back into the second equation:
y = 11(1.95)
y = 21.45
Therefore, the larger number is 21.45.