A salesperson earns $350 per week plus 10% of her weekly sales. Find the sales neccesary for the salesperson to earn at least $800 in one week

Question

solve each problem by writing an inequality. 

Answer 1

Hi Alexa,

 

Let's begin by assigning a letter to represent our unknown:

    x = sales necessary to earn $800 in one week

 

Now let's first write the earning equation in words:

    Salary + Commission = Earnings

 

Now let's replace the words in the equation with our mathematical expressions:

    Salary + Commission = Earnings

    350 + (0.10)(x) = 800

 

Now let's write an inequality based upon our equation by replacing the equal sign with the greater than or equal sign, indicating that we need to at least reach our target Earnings:

    350 + (0.10)(x) ≥ 800

 

Finally, we'll solve our inequality with standard algebraic techniques just like we would solve an equation: 

    350 + (0.10)(x) ≥ 800

    350 + 0.10x ≥ 800

             0.10x ≥ 800 - 350

             0.10x ≥ 450

                   x ≥ 450/0.10

                   x ≥ $4500

 

So we see that to reach a weekly earnings amount of $800 in one week, a salesperson would need to have at least $4500 in sales that week.

 

The key to remember in solving inequality word problems is to first know what kind of inequality relationship the problem is asking for and then to set up and solve the inequality just like we would do for an equation.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.