a wholesaler bought 1200 radios for $18 each. the wholesaler

[rkafc81]

a wholesaler bought 1200 radios for $18 each. the wholesaler sold 60% of the radios for $30 each and the rest for $15 each. what was the wholesaler's average (arithmetic mean) profit per radio?

a) $2
b) $3
c) $4
d) $5
e) $6








oe: e


i found this to be deceptively tricky and prone to error due to the excessive amounts of calculations required and 'pieces of the puzzle' to solve. would be the best way to solve this ? i tried splitting all the info out into a chart with each distinct entity in the question being a column, and then ran out of time... :(

thanks

[aliassad]

Nah . You do not need any heavy calculation .

Just understand the concept of weighted average.

First step calculate the average profit per radio .

Note the weights are 60% (or 6) for the price of $30 and 40% (or 4) for the price of $ 15.

The average profit rate wil be between $15 and $ 30. But where?
Note the$ 30 price radios are more heavily weighted. So the average should be closer to $ 30. Here is the key:

In weighted averages there are two concepts : weights and distances. They are inversely proportional.

So it means the distance of average from $15 will be 6 units wheres the distance of average from $ 30 will be 4. Total distance is $15 (30-15) and corresponds to 10 units.This implies that 1 unit is equial 1.5$ so average if $ 6*1.5 above $ 15 price and $4*1.5 below the $ 30 price. In both cases the value comes to $ 24.

With practice the above approach should take you not more than 30 seconds.


Ali Asad

[dw6586]

totally agree with the previous commenter about using the weighted averages shortcut. when they give u info about the total, averages and a percent/ratio breakdown ... they are looking for some sort of average, and to be tricky, it will usually be weighted averages.

to avoid hefty calculation, my method is similar to the person who described it above, but i break it down to ratios because that works better in my mind. you know the percent of each radio pricing, 60% and 40% so you know the ratio between the two different sales is 6:4 or further, 3:2. now you treat that as you would any weighted averages problem. [3($30) + 2($15)] / 5 = $24 average revenue. (the denominator, 5, comes from the total 3+2 btw). Then from there, you know the average profit would be $24-$18 = $6.

the trick is recognizing what they are looking for before plugging in all the numbers and doing long calculations. any sort of total cost and percent/ration breakdown of averages usually means there is a shortcut to figuring it out using weighted averages.

hope this helps clarify.

[jnelson0612]

You two have provided two excellent methods. Thank you for your posts! :-)

[RonPurewal]

i don't think this problem involves excessive calculation, even if you go about it the long way. after all, the numbers are not that bad; if the calculations in this problem actually do take you a long time, then you may want to spend a little bit of time just practicing pure arithmetic.

more importantly, i'm curious what you found "deceptively tricky" (your words) about this problem, because this is one of the few problems i've seen that is totally literal and rather straightforwardly stated, without any unexpected twists, turns, or things to decode.
i.e., "average profit per unit" is total profit divided by the number of units. (this definition is not exclusive to profit; average = sum/total is a very generalizable equation.) since the number of units (1200) is given, you basically just have to find the total profit.

profit is revenue minus cost.
the total revenue was 720(30) + 480(15) = 21600 + 7200 = 28800.
the total cost was 1200(18) = 21600.
so total profit is 28800 - 21600 = 7200.

so, profit per unit is 7200/1200 = $6.

provided that you are decently familiar with the concepts of "average" and "profit" (two things with which you should be VERY familiar, if you aren't already), this should be less than two minutes' worth of calculation.

the weighted-average shortcuts listed earlier in this thread will also work, but it's important not to become too dependent on such tricks. there are more problems than you might think on which you can just grind out an answer with arithmetic, so you should certainly be able to do so.