Solve the problem using the six-step method: a pharmacist found at the end of the day she had 7/4 as many prescriptions for antibiotics as tranquilizers. she had 33 prescriptions altogether. how many did she have for tranquilizers?

1 (female) pharmacist counting prescriptions at the end of the day

(prescriptions for antibiotics) = (7/4)×(prescriptions for tranquilizers)

33 = (prescriptions for tranquilizers) + (prescriptions for antibiotics)

The number of (prescriptions for tranquilizers)

Let x represent the number of prescriptions for tranquilizers. Then the number of prescriptions for antibiotics is (7/4)x, and the total number of prescriptions is

... 33 = x + (7/4)x . . . . . . . . . . put the given information in the given relation

... 33 = (4/4)x + (7/4)x . . . . . . rewrite 1 as 4/4 so we can add to 7/4

... 33 = ((4+7)/4)x = (11/4)x . . . simplify

... 33×(4/11) = (4/11)×(11/4)x . . . multiply by the reciprocal of the coefficient of x

... 12 = x . . . . . . . . . . . . . . . . . simplify

The pharmacist had 12 prescriptions for tranquilizers.

The pharmacist had 33-12 = 21 prescriptions for antibiotics.

There was 1 pharmacist and 33 prescriptions.