Carcass wrote:
Last September the sales total for a certain car dealership was 400% greater than the average monthly sales total for the other 11 months. The sales total for September was approximately what percent of the year´s sales?
A. 15 %
B. 27%
C. 31%
D. 42%
E. 75%
Kudos for the right answer and explanation
Here's the algebraic solution.
Let x = the total sales for January
Let x = the total sales for February
Let x = the total sales for March
.
.
Let x = the total sales for August
Let x = the total sales for October
Let x = the total sales for November
Let x = the total sales for December
NOTE: We haven't yet assigned an expression for the total sales in SeptemberAverage monthly sales for the 11 months (excluding September) = (x+x+x+x+x+x+x+x+x+x+x)/11 = 11x/11 = x
Last September the sales total for a certain car dealership was 400% [b]greater than the average monthly sales total for the other 11 months. [/b]
Average monthly sales for the 11 months = x
The total sales for September = x + (400% of x) = x + 4x =
5x The sales total for September was approximately what percent of the year´s sales? TOTAL sales for the year = x+x+x+x+x+x+x+x+x+x+x +
5x =
16xSo, we need to convert
5x/
16x into a PERCENT
5x/
16x = 5/16, so one approach is to use long division to divide 16 into 5, and then convert that decimal to a percent.
Alternatively, we can use some estimation.
Take 5/16 and multiply a numerator and denominator by 6 we get the equivalent fraction 30/96
We know that 30/100 = 30%
Since the denominator, 96, is slightly less than 100, we know that 30/96 is slightly greater than 30%
Answer: C