Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 3. Find the larger integer.  Choose the correct choice from the following answers
A) 4	B) 24	C) 30	D) 72	E) 80
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 6 to the smaller integer makes the ratio 1 to 3, then 3(x+6)=y.   Substituting y=4x into the second equation yields 3x+18=4x.   So, x=18 (smaller integer) and, y=4x=72 (larger integer) so D is the correct answer.   Another option is to TEST the answer choices.   A) the larger number is 4   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 1   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (1), we get 7.   So, the new ratio is 7 to 4.   No good. We want a resulting ratio of 1 to 3   ELIMINATE A   B) the larger number is 24   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 6   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (6), we get 12   So, the new ratio is 12 to 24 which is 1 to 2.   No good. We want a resulting ratio of 1 to 3   ELIMINATE B   C) the larger number is 30   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 7.5 (which is not an integer)   Since both numbers are integers, the larger number cannot be 30.   ELIMINATE C   D) the larger number is 72   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 18   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (18), we get 24   So, the new ratio is 24 to 72. This is the same as the ratio of 1 to 3   Therefore (D) is correct   E) the larger number is 80   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 20   If 6 is added to the smaller number, the ratio becomes 1 to 3   If we add 6 to the smaller number (20), we get 26   So, the new ratio is 26 to 80 which is 13 to 40.   No good. We want a resulting ratio of 1 to 3   ELIMINATE E   Therefore 72 is the only correct choice.
<result>D</result>
Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 3. Find the larger integer.