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# [Smart Math] Percentages Problem 28

Here’s and example of a SMART MATH problem for PERCENTAGES. ### Problem

A salesman gets a flat commission of 10% on all sales and a bonus of 2.5% on all sales exceeding $10,000. If in a particular month he earns$2875, what were his sales worth?

1. $35,000 2.$23,000
3. $25,000 4.$15,000
5. $24,000 ### The Usual Method [contentblock id=google-adsense-post] Let the sales be worth$‘x’. (Assume x > $10,000) Hence commission = $\frac{10}{100}x=0.1x$ And Bonus = $\frac{2.5}{100}\times (x-10000)=0.025x-250$ Hence total earnings = $0.1x+0.025x-250=2875$ $\therefore 0.125x=3125$ $\therefore x=\frac{3125}{0.125}=$$25,000

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Since the total commission earned is more than $1000, ($2875), the sales has to be more than $10,000 (Since 10% of$10,000 = $1000). Hence any additional commission is attributable to sales worth over$10,000. Thus, 2875 – 1000 = 1875 is the commission earned on sales over $10,000. Note that the salesman continues to earn 10% commission along with the bonus of 2.5%. Hence total commission earned on sales over$10,000 = 10 + 2.5 = 12.5%. Thus $1875 is 12.5% of sales over$10,000. Hence, value of sale over $10,000 = $\frac{1875}{12.5}\times 100=$$15,000. Hence total sales are worth 10,000 + 15,000 = \$25,000