A pharmacist found at the end of the day she had seven fourths
7/4 as many prescriptions for antibiotics as tranquilizers. She had 44 prescriptions altogether. How many did she have for tranquilizers?
44/(7+4) = 44/11 = 4
7 * 4 = 28
4 * 4 = 16
16 + 28 = 44
Let's assume the number of prescriptions for tranquilizers is x.
According to the given information, the number of prescriptions for antibiotics is 7/4 times the number of prescriptions for tranquilizers. So, the number of prescriptions for antibiotics would be (7/4)x.
The total number of prescriptions is the sum of the prescriptions for tranquilizers and antibiotics. Therefore, we have the equation x + (7/4)x = 44.
To solve for x, we can combine like terms and solve the equation: 4x + 7x/4 = 44.
Multiplying through by 4 to eliminate the fraction, we get 16x + 7x = 176.
Combining like terms, we have 23x = 176.
Finally, we can solve for x by dividing both sides of the equation by 23: x = 176/23.
So, the pharmacist had 176/23 ≈ 7.65 prescriptions for tranquilizers. Rounding to the nearest whole number, the pharmacist had about 8 prescriptions for tranquilizers.
To solve this problem, we need to set up an equation based on the given information. Let's assume the number of prescriptions for tranquilizers is 'x'.
We are told that the pharmacist had 7/4 as many prescriptions for antibiotics as tranquilizers. This means the number of prescriptions for antibiotics would be (7/4) * x.
According to the problem, the pharmacist had a total of 44 prescriptions. Therefore, we can write the equation as:
x + (7/4)x = 44
Now, let's solve the equation to find the value of x, which represents the number of prescriptions for tranquilizers.
Multiplying through by 4 to eliminate the denominator, we get:
4x + 7x = 44 * 4
11x = 176
Dividing both sides by 11, we find:
x = 176/11
x = 16
So, the pharmacist had 16 prescriptions for tranquilizers.
Therefore, she had 16 prescriptions for tranquilizers and (7/4) * 16 = 28 prescriptions for antibiotics.