A local salesman receives a base salary of $900 monthly. He also receives a commission of 7% on all sales over $1000. How much would he have to sell in a month if he needed to have a monthly income of $2900?
900 + .07(x-1000) = 2900
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To find out how much the salesman would have to sell in a month, let's break it down into steps:
Step 1: Calculate the income from the base salary: $900
Step 2: Calculate the remaining income needed: $2900 - $900 = $2000
Step 3: Calculate the amount of sales required to generate the remaining income:
Let's assume the amount of sales required to generate the remaining income is x.
Commission on sales over $1000 = 7% of (sales - $1000) = 0.07 * (x - $1000)
Step 4: Set up an equation:
Commission on sales over $1000 = Remaining income needed
0.07 * (x - $1000) = $2000
Step 5: Solve the equation for x:
0.07 * (x - $1000) = $2000
(x - $1000) = $2000 / 0.07
x - $1000 = $28571.43
x = $28571.43 + $1000
x ≈ $29571.43
Therefore, the salesman would have to sell approximately $29571.43 in a month to have a monthly income of $2900.
To find out how much the salesman would have to sell in a month to have a monthly income of $2900, we need to consider both his base salary and the commission he receives on sales over $1000.
Let's start by calculating the commission he receives on sales over $1000. We know that the commission rate is 7%. So, if he sells an amount S over $1000, his commission income would be 7% of S.
Next, we need to determine the amount of sales that would result in the desired monthly income, taking into account the base salary and the commission income.
Let's break it down into two cases:
Case 1: If the total sales (S) do not exceed $1000, the commission income would be $0, and the monthly income would simply be the base salary of $900. In this case, the salesman needs the remaining monthly income to be $2900 - $900 = $2000.
Case 2: If the total sales (S) exceed $1000, the commission income would be 7% of (S - $1000). In this case, the salesman needs the sum of the base salary and the commission income to be $2900.
To summarize, we have two equations:
Case 1: $900 + $0 = $2000
Case 2: $900 + 7% of (S - $1000) = $2900
Now, let's solve these equations to find the amount of sales that would result in the desired monthly income.
In Case 1, we have $900 = $2000, which is not a valid equation.
In Case 2, we have $900 + 0.07(S - $1000) = $2900.
Simplifying this equation, we get 0.07(S - $1000) = $2900 - $900,
which further simplifies to 0.07S - $70 = $2000,
and after isolating the variable, we have 0.07S = $2070.
Dividing both sides by 0.07, we obtain S = $29,571.43.
Therefore, the salesman would have to sell approximately $29,571.43 in a month to have a monthly income of $2900.