Apply mathematical principles to solve a real-world problem.

Question

An electronics store has a current inventory of 50 stereo systems. The lowest priced stereo system in the store sells for 800 dollars, and the highest priced stereo system sells for $3000 dollars. Which of the following is the maximum amount of $3000 systems on hand if the current inventory totals $111,000?

Answer 1

30 highest priced stereos would be 30 x $3000 = $90,000 The remaining $21,000 (111000-90000) divided by $800 = 26+

30+26>50. To get down to just 50 stereos some of the remaining 20 are not the lowest priced, but intermediately priced.

35 highest priced would be 35x$3000= $105000 The remaining $6,000 divided by $800 = 7 1/2. That's

too small. 35 + 7.5 <50. It's not possible to have 35 highest priced stereos in the current inventory.

the maximum number of highest priced stereos is somewhere between 30 and 34, try the midpoint.

32 x $3000 = $96,000 The remaining $15000 divided by $800 = 18 3/4

this is possible, as 32 + 18 =50. Some of the 18 will have to be intermediately priced though to total $15000. The solution is either 32 or 33.

33 x$3000 = $99000 The remaining $12000 divided by $800 = 15 33+15=48 < 50. 33 is more than

the maximum possible.

The answer is 32 highest priced stereos is the maximum amount if the current inventory totals $111,000 and the total number of stereos is 50.