Algebra problem [children encouraged ...]
I'm looking for a 6th grader to write out a math equation for me.
Here are the details.
To make bonus when selling apples, Johnny has to average $20 for each of the sales appointments he is assigned for the month. [Five appointments, with one $100 sale, equal $20 per assignment].
When selling oranges, an orange salesman has to average $17 per sale.
Johnny went on twenty apple appointments last month, and had an average sale of $23.
Johnny also went on seven orange appointments, with an average sale of $32.
What is the weighted average required to make bonus, given the $20 dollar-per-lead of apple sales, and the $17-per-lead of orange sales, as expressed in an algebraic equation?
Here are the details.
To make bonus when selling apples, Johnny has to average $20 for each of the sales appointments he is assigned for the month. [Five appointments, with one $100 sale, equal $20 per assignment].
When selling oranges, an orange salesman has to average $17 per sale.
Johnny went on twenty apple appointments last month, and had an average sale of $23.
Johnny also went on seven orange appointments, with an average sale of $32.
What is the weighted average required to make bonus, given the $20 dollar-per-lead of apple sales, and the $17-per-lead of orange sales, as expressed in an algebraic equation?
0
-
Not for sure what you are asking but
If X is the $ amount of apples sold
(X/20)=23 X= 460 The total sales in apples was $460
If Y is the $ amount of oranges sold.
(Y/7)=32 Y=224 The total sales in oranges was $224.
For him to meet the minimum it is
(X/#of sales calls)> $20
(Y/#of sales calls)> $170 -
The weighted average depends on what proportion of sales are apple sales and what proportion are orange sales.
Let X be the proportion of sales that are apple sales.
Then 1-X = the proportion of sales that are orange sales.
Weighted average to make bonus (B) is
B = 20 * X + 17 * (1-X). Simplifying:
B = 3X + 17.
Is that what you wanted?
Edit: oops. I see you were looking for children to answer that. It seems to me like a tough one for a sixth grader. Actually, I think a lot of the college freshman I teach would have trouble with that (not that they should....they just would).0 -
As you say, spurge, it depends on the ratio.
And you never know what the ratio might be, as it can change month by month.
I can figure it out through a complicated back-door method using proportions,
but I was interested in a simple fits-all equation.
I still can't quite wrap my head around it. The variables include the ratio between the different items sold, and the differing average sale, depending on product.
Where's Kristov?0 -
quote:Originally posted by Sperry
I'm looking for a 6th grader
and there are plenty on this forum.0 -
Comparing apples to oranges is just bad business [:)]. 0 -
quote:Originally posted by Sperry
As you say, spurge, it depends on the ratio.
And you never know what the ratio might be, as it can change month by month.
I can figure it out through a complicated back-door method using proportions,
but I was interested in a simple fits-all equation.
I still can't quite wrap my head around it. The variables include the ratio between the different items sold, and the differing average sale, depending on product.
Where's Kristov?
If you're really looking for something that is useful to a salesman, the best strategy will be to maximize each sale.
If you're looking for a predictor of what will be necessary to achieve bonus, then there is no deterministic solution because proportions will vary from month to month and probably from year to year.
Given enough historical data, it would be possible to build a statistical model that would predict what the weighted average should be to achieve the bonus SOME PERCENTAGE of the time.
I would want ten years of data on the following variables, if I were attempting such a model:
1) # orange sales for each month of the year.
2) # apple sales for each month of the year
3) apple wholesale price each month of the year
4) orange wholesale price each month of the year
5) some measure of consumer confidence each month of the year.
Given month by month data on those five things for the past ten years, I think it would be possible to build a pretty good predictive model of what your weighted average sale should be to achieve bonus 95% of the time.0 -
spurge, it ain't that hard.
In my simple example, I figure the weighted average to be $19.22
{[20 times $20] + [7 times $17]} ? 27
... if I'm doing it right.
Maybe this is the answer:
{[Number of appointments] * [required average for product 1]} PLUS
{[Number of appointments] * [required average for product 2]} DIVIDED BY
total appointments run.
I'll run it through some examples at work.0 -
quote:Originally posted by Sperry
spurge, it ain't that hard.
In my simple example, I figure the weighted average to be $19.22
{[20 times $20] + [7 times $17]} ? 27
... if I'm doing it right.
Maybe this is the answer:
{[Number of appointments] * [required average for product 1]} PLUS
{[Number of appointments] * [required average for product 2]} DIVIDED BY
total appointments run.
I'll run it through some examples at work.
You're right. I over-read your question. I get the same answer too, both by your calculations and by my formula:
Proportion of apple sales = 20/27 = 0.7407.
B = 3 * X + 17
= 3 * .7407 + 17
= 2.22 + 17
= 19.22
and
quote:{[Number of appointments] * [required average for product 1]} PLUS
{[Number of appointments] * [required average for product 2]} DIVIDED BY
total appointments run.
is precisely equal to the equation I just used.0 -
quote:Originally posted by kristov
Comparing apples to oranges is just bad business [:)].
For once I am impressed with your simplicity.0
Please sign in to leave a comment.
Comments
9 comments