The sum of two numbers is 156. The excess of 4 times the larger over 4 times the smallest is 75. What are the numbers?
OK, let's see if we can disentangle this.
We have: The excess of 4 times the larger over 4 times the smaller is 75.
Let X = 4 times the larger.
Let Y = 4 times the smaller.
Then we now have,
The excess of X over Y is 75.
A reasonable interpretation of the above line would be,
X - Y = 75, or
4L - 4S = 75 (L is the larger number, S is the smaller number)
L - S = 75/4 = 18.75, and
L + S = 156 (The sum of two numbers is 156)
Adding together the above two equations,
2L = 174.75
L = 87.375, S = 68.625