Question

As a pharmacist, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 110 milligrams of Medication A with 154 milligrams of Medication B. However this week, the doctor said to only use 126 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

Answer 1

110/154 = x/126

154x/13860

x = 13860 /154 = 90

 90 milligrams of medicine A

Answer 2

Set up a proportion:

$\frac{110}{154} = \frac{x}{126}$

The numerator represents the amount of Medication A, and the denominator represents the amount of Medication B.

The first fraction can be simplified by finding the GCF (greatest common factor) of 110 and 154:

$\text{gcf(110,154) = 22}$

Divide both the numerator and denominator of the first fraction by the GCF:

$\frac{110}{154} \div \frac{22}{22} = \frac{5}{7}$

$\frac{5}{7} = \frac{x}{126}$

Cross multiply:

$7x = 630$

Divide both sides by 7 to get x by itself:

$x = 90$

90 milligrams of Medication A should be mixed this week.