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 .
"one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = 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 = 4 x into the second equation yields 3 x + 18 = 4 x . so , x = 18 ( smaller integer ) and , y = 4 x = 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 can not 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 d is the only correct choice ."
multiply(divide(multiply(3, 6), subtract(4, 3)), 4)