Question 1160146
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Since many students dislike working with fractions, here is another way to set up and solve this problem.<br>
The statement of the problem says there are 4/3 as many prescriptions for antibiotics as there are for cough medicines.  A direct translation of that information into algebraic expressions would have x as the number of prescriptions for cough medicines and (4/3)x for the number of prescriptions for antibiotics.<br>
A different approach would be to translate the "....4/3 as many..." into "...a ratio of 4:3...".  Then we can use 3x for the number of prescriptions for cough medicines and 4x for the number of prescriptions for antibiotics.<br>
Now the algebra is easier:<br>
{{{3x+4x = 84}}}
{{{7x = 84}}}
{{{x = 84/7 = 12}}}<br>
The number of prescriptions for cough medicines is 3x = 3(12) = 36.<br>