SOLUTION: A drug store sells three categories of items: A. Medicine, which is not taxed B. Non-medical items, which are taxed at the rate of 8% C. Beer and cigarettes, which are taxe

Question 1030958: A drug store sells three categories of items:
A. Medicine, which is not taxed
B. Non-medical items, which are taxed at the rate of 8%
C. Beer and cigarettes, which are taxed at the "sin tax" rate of 20%
Last Friday, the total sales (excluding taxes) of all three items were $18,500. The tax collected was $1,020. The sales of medicines exceeded the combined sales of the other items by $3500. Find the sales in each category.
Need three linear equations.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A. Medicine, which is not taxed SALES --------X
B. Non-medical items, which are taxed at the rate of 8%--------------Y
C. Beer and cigarettes, which are taxed at the "sin tax" rate of 20%---------Z
Last Friday, the total sales (excluding taxes) of all three items were $18,500.
X+Y+Z=18500...............(1)
The tax collected was $1,020.
8%Y+20%Z=1020.....................(2)
MULTIPLY BY 100
8Y+20Z=102000
The sales of medicines exceeded the combined sales of the other items by $3500.
X-3500 = y+z......................(3)
X+(Y+Z)= 18500
X+(X-3500)=18500
2X = 18500+3500
2X= 22000
X= 11,000
Now
8Y +20Z=102000..............4
y+z=7500
8y+8z= 60000.................5
(4-5)
12z=42000
z=3500
y+z=7500
z=3500
y= 4000
Medicine --------------$11,000
B. Non medical -------$4000
C. Beer and cigarettes, $3,500

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