Question

reasoning a salespersons commission rate is 4%. what is the commission from the sale of $34,000 worth of furnaces? use pencil and paper. suppose sales would double. what would be true about the commission? explain without using any calculations.
the commission is $□

Explanation:

Step1: Recall the formula for commission

Commission = Commission rate × Sales amount.

Step2: Substitute the values

Given commission rate \(r = 4\%\) or \(0.04\) and sales amount \(S=\$34000\). Commission \(C=0.04\times34000\).

Step3: Analyze without calculation

Since \(4\%\) of \(10000\) is \(400\), \(4\%\) of \(34000\) is \(3.4\) times \(400\) (because \(34000 = 3.4\times10000\)). So \(C = 3.4\times400=\$1360\).
If sales double (\(S'= 2\times34000 = 68000\)), and commission rate \(r\) remains \(4\%\), using the formula \(C'=r\times S'\), since \(S' = 2S\), \(C'=2\times(r\times S)\) (by the property of multiplication \(a\times(b\times c)=(a\times b)\times c\) where \(a = 2\), \(b=r\), \(c = S\)). So the new commission is double the original commission.

Answer:

The commission is \(\$1360\). If sales double, the commission also doubles.