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

**Problem**

**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?

- $35,000
- $23,000
- $25,000
- $15,000
- $24,000

**The Usual Method**

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Let the sales be worth $‘*x*’. (Assume *x* > $10,000)

Hence commission =

And Bonus =

Hence total earnings =

$25,000

**(Ans: 3)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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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 = $15,000. Hence total sales are worth 10,000 + 15,000 = $25,000

**(Ans: 3)**

*Estimated Time to arrive at the answer = 15 seconds.*

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