## A pharmacist found at the end of the day she had 3/2 as many prescriptions for antibiotics as tranquilizers. She had 35 prescriptions altoge

Question

A pharmacist found at the end of the day she had 3/2 as many prescriptions for antibiotics as tranquilizers. She had 35 prescriptions altogether. How many did she have for tranquilizers?

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1 year 2021-08-31T15:12:04+00:00 1 Answers 0 views 0

She had 14 prescriptions for tranquilizers.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of prescriptions she had for antibiotics.

y is the number of prescriptions she had for tranquilizers.

A pharmacist found at the end of the day she had 3/2 as many prescriptions for antibiotics as tranquilizers.

This means that:

$$\frac{x}{y} = \frac{3}{2}$$

$$x = \frac{3y}{2}$$

This means that:

$$x + y = 35$$

How many did she have for tranquilizers?

We want to find y. Since $$x = \frac{3y}{2}$$, we solve the following equation.

$$x + y = 35$$

$$\frac{3y}{2} + y = 35$$

Multiplying everything by 2

$$3y + 2y = 70$$

$$5y = 70$$

$$y = \frac{70}{5}$$

$$y = 14$$

She had 14 prescriptions for tranquilizers.