Two number have a difference of 10. The sum of the larger one and two thirds of the smaller number is 16. What are these two numbers?
Let's call the larger number x and the smaller number y.
According to the first statement, the difference between the two numbers is 10: x - y = 10.
According to the second statement, the sum of the larger number and two thirds of the smaller number is 16: x + (2/3)y = 16.
We can solve this system of equations by substitution or elimination. Let's use substitution here.
From the first equation, we can rewrite it as x = y + 10.
Substitute this expression for x in the second equation: (y + 10) + (2/3)y = 16.
Now we can solve for y:
2/3y + y + 10 = 16
5/3y + 10 = 16
5/3y = 6
y = 6 * 3/5
y = 18/5
y = 3.6
Now substitute the value of y back into the first equation to solve for x:
x = 3.6 + 10
x = 13.6
So the two numbers are 3.6 and 13.6.