Question

A salesperson earns commission on the sales that she makes each mouth.The sales person earns 5% commissions on the first $5,000 she has in sales. The sales person Earns 7.5% commissions on the amount of her sales that are greater than $5,000. The sales person Earns $1,375 in last month.How much money in dollars did she have in sales last month?

Answer 1

We have that we can represent the total sales with the following expression:

`\text{total sales=ssales with 5\% comission + sales with 7\% comission}_{}`

Now, we have that the sales person earns 5% comission on the first $5000, this is equivalent to:

`5000\cdot(0.05)=250`

then, if the salesperson earns $1375 in comissions, we have the following equations:

`\begin{gathered} \text{7.5\% comission = total comissions-5\% comissions} \\ \Rightarrow\text{ 7.5\% comission = 1375-250=1125} \end{gathered}`

we have that the sales with 7.5% comissions got the salesperson $1125, then, we have the following:

`\text{sales with 7.5\% = }\frac{7.5\text{ \% comission}}{7.5\text{ \%}}=(1125)/(0.075)=15000`

therefore, the salesperson had 15000+5000=$20000 in sales to earn $1375 in comissions