A stationery supplier ordered 10 boxes of deluxe pens and some boxes of regular pens. The price of deluxe pens per box was three times that of regular pens. When the order was delivered, the number of boxes of deluxe and regular pens had been accidentally interchanged. This decreased the total bill by 50%. What was the ratio of the original number of boxes of deluxe pens to the original number of boxes of regular pens?
Show answer & explanation
Correct answer: C
Explanation
Let regular pen price = x, so deluxe pen price = 3x
Let original regular boxes = r, deluxe boxes = 10
Original bill = 10(3x) + r(x) = 30x + rx
After interchange: deluxe boxes = r, regular boxes = 10
New bill = r(3x) + 10(x) = 3rx + 10x
Given: New bill = 50% less than original bill
3rx+10x=0.5(30x+rx)3rx + 10x = 0.5(30x + rx)3rx+10x=0.5(30x+rx) 3r+10=15+0.5r3r + 10 = 15 + 0.5r3r+10=15+0.5r 2.5r=52.5r = 52.5r=5 r=2r = 2r=2
Original ratio (deluxe : regular) = 10 : 2 = 5 : 1 ✓