Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.  Choose the correct answer.
A) 8
B) 16
C) 32
D) 48
E) 54
One option is to set up the equations and solve:   If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.   If adding 12 to the smaller integer makes the ratio 1 to 1, then x+12=y.   Substituting y=4x into the second equation yields x+12=4x.   So, x=4 (smaller integer) and, y=4x=16 (larger integer) so B is the correct answer.   Another option is to TEST the answer choices.   A) the larger number is 8   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 2   If 12 is added to the smaller number, the ratio becomes 1 to 1   If we add 12 to the smaller number (2), we get 14.   So, the new ratio is 14 to 8 which is the same as 7 to 4.   No good. We want a resulting ratio of 1 to 1   ELIMINATE A   B) the larger number is 16   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 4   If 12 is added to the smaller number, the ratio becomes 1 to 1   If we add 12 to the smaller number (4), we get 16   So, the new ratio is 16 to 16 which is 1 to 1.   Therefore (B) is correct.   C) the larger number is 32   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 8   If 12 is added to the smaller number, the ratio becomes 1 to 1   If we add 12 to the smaller number (8), we get 20   So, the new ratio is 20 to 32 which is 5 to 8.   No good. We want a resulting ratio of 1 to 1   ELIMINATE C   D) the larger number is 48   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 12   If 12 is added to the smaller number, the ratio becomes 1 to 1   If we add 12 to the smaller number (12), we get 24   So, the new ratio is 24 to 48. This is the same as the ratio of 1 to 2   No good. We want a resulting ratio of 1 to 1   ELIMINATE D   E) the larger number is 54   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 13.5 (which is not an integer)   Since both numbers are integers, the larger number cannot be 54.   ELIMINATE E   Therefore 16 is the only correct choice.
<result>B</result>
Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.