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## 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

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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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Mathematics
1 year
2021-08-31T15:12:04+00:00
2021-08-31T15:12:04+00:00 1 Answers
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## Answers ( )

Answer: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:

[tex]\frac{x}{y} = \frac{3}{2}[/tex]

[tex]x = \frac{3y}{2}[/tex]

She had 35 prescriptions altogether.This means that:

[tex]x + y = 35[/tex]

How many did she have for tranquilizers?We want to find y. Since [tex]x = \frac{3y}{2}[/tex], we solve the following equation.

[tex]x + y = 35[/tex]

[tex]\frac{3y}{2} + y = 35[/tex]

Multiplying everything by 2

[tex]3y + 2y = 70[/tex]

[tex]5y = 70[/tex]

[tex]y = \frac{70}{5}[/tex]

[tex]y = 14[/tex]

She had 14 prescriptions for tranquilizers.