SOLUTION: One employee of a computer store is paid a base salary of ​$4000 a month plus 8 ​% commission on all sales over ​$6000 during the month. How much must the employee sell in on

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Question 1196254: One employee of a computer store is paid a base salary of ​$4000 a month plus 8 ​% commission on all sales over ​$6000 during the month. How much must the employee sell in one month to earn a total of ​$5000 for the​ month?
Write an equation required to find the​ solution, using x to represent the amount of​ sales, in​ dollars, by the employee.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

    4000 + 0.08(x-6000) = 5000

    0.08*(x-6000) = 5000 - 4000

    0.08*(x-6000) =    1000

         x - 6000 =    1000/0.08 = 12500

         x                       = 12500 + 6000 = 18500.    ANSWER

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = amount in sales (in dollars)

The employee earns 8% commission on sales over $6000
This means that if their sales are $6000 or smaller, then they earn no commission. They only have the base salary of $4000

The expression (x-6000) represents the difference in sales with the $6000 target. If x > 6000, then x-6000 is some positive value.
Example: If you made $7200 in sales, then x-6000 = 7200-6000 = 1200 dollars is the amount where the 8% commission kicks in.

The expression 0.08(x-6000) is the extra amount earned in commission.
Example: If you made $7200 in sales, then you earn an extra 0.08*(x-6000) = 0.08*(7200-6000) = 96 dollars on top of the $4000 base salary.
In other words, you earn 8% on the 1200 extra sales, so 8% of 1200 = 0.08*1200 = 96
The total monthly pay is 4000+96 = 4096 dollars.

The expression 4000+0.08(x-6000) is the total amount earned where x > 6000
If x = 6000 or smaller, then the employee simply earns $4000 with no extras.

But since we want the employee to earn $5000 per month, we need to have x > 6000 be the case.

Set 4000+0.08(x-6000) equal to the goal of 5000 and solve for x.

4000+0.08(x-6000) = 5000
0.08(x-6000) = 5000-4000
0.08(x-6000) = 1000
x-6000 = 1000/(0.08)
x-6000 = 12500
x = 12500+6000
x = 18500

An alternative way to solve that previous equation.
4000+0.08(x-6000) = 5000
4000+0.08x-0.08*6000 = 5000
4000+0.08x-480 = 5000
0.08x+3520 = 5000
0.08x = 5000-3520
0.08x = 1480
x = 1480/(0.08)
x = 18500


Check:
The employee made $18,500 in sales
Subtract off $6000 to find how much of that money is when the commission kicks in.
18500 - 6000 = 12500
8% of that is 0.08*12500 = 1000
The employee earns an extra $1000 on top of the $4000 base salary, so we achieve the goal of 4000+1000 = 5000 dollars per month that we're after.
The answer is confirmed.


Answer: $18,500 in sales
Delete the dollar sign and/or comma if needed.