A pharmaceutical company sells bottles of 500 calcium tablets in two dosages: 250 milligram and 500 milligram. Last month, the company sold 2,200 bottles of 250-milligram tablets and 1,800 bottles of 500-milligram tablets. The total sales revenue was $39,200. The sales team has targeted sales of $44,000 for this month, to be achieved by selling of 2,200 bottles of each dosage. Assume that the prices of the 250-milligram and 500-milligram bottles remain the same.

Determine the price of a 250-milligram bottle as well as the price of a 500-milligram bottle.

Question

Mathematics

Christine

29 April, 22:13

A pharmaceutical company sells bottles of 500 calcium tablets in two dosages: 250 milligram and 500 milligram. Last month, the company sold 2,200 bottles of 250-milligram tablets and 1,800 bottles of 500-milligram tablets. The total sales revenue was $39,200. The sales team has targeted sales of $44,000 for this month, to be achieved by selling of 2,200 bottles of each dosage. Assume that the prices of the 250-milligram and 500-milligram bottles remain the same.

Determine the price of a 250-milligram bottle as well as the price of a 500-milligram bottle.

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Answers (1)

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Davian · Answer 1

Let x and y be the prices of the 250 milligram and 500 milligram dosage, respectively. The equations that may be derived from the given conditions above are,

2200x + 1800y = 39200

2200x + 2200y = 44000

Solving the system by subtracting the second equation from the first gives,

-400y = - 4800; y = 12

Substitute the obtained value for y in either of the equations. I choose the first equation,

2200x + (1800) (12) = 39200

2200x = 17600; x = 8

Thus, the 250-mg bottle costs $8 and each 500-mg bottle costs $12.