Cheese12 wrote:A salesman sells two equally priced brands of icecream, for which he receives a sales commission of 5 percent on one brand and 7 percent on the other. If the salesman sold a total of $10,000 in icecream and collected $660 in commissions, what fractional part of the total icecream sold did he sell at the lower commission rate?
A) 7/8
B) 4/5
C) 1/2
D) 1/5
E) 1/8
Answer : D
please give a quick method to solve this one...thanks!
This is a weighted average question.
660/10,000 = 6.6%.
A 5% commission is being combined with a 7% commission to yield a mixture with a 6.6% commission.
We can use alligation:
The proportion of each element in the mixture is equal to the distance between the OTHER two percentages.
Proportion of 5% commission = distance between 7% and 6.6% = |7-6.6| = .4
Proportion of 7% commission = distance between 5% and 6.6% = |5-6.6| = 1.6.
Ratio of 5% to 7% in the mixture = (.4) : (1.6) = 4:16= 1:4.
The sum of the parts of the ratio = 1+4 = 5
Thus, for every $5 earned, $1 comes from the lower rate, $4 comes from the higher rate.
Fraction from the lower rate = 1/5.
The correct answer is
D.
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