Use symbols to represent unknowns and variables. Write inequalities to answer questions arising situations.
1. A sales representative is given a choice of two paycheck plans. One choice includes a monthly base pay of $300 plus %10 comission on his sales. The second choice is a monthly salary of $1200. For what amount of sales would the representative make more money with the first plan?
0.1x > 900
x > 900/0.1
x > $9,000
I don't understand where 900 comes from...
To answer this question, we need to set up an inequality that represents the condition where the first paycheck plan earns the representative more money.
Let's say the amount of sales is represented by the variable "s".
Under the first plan, the representative earns a monthly base pay of $300 plus 10% commission on his sales. So, the first plan's monthly earnings can be represented as:
Earnings = $300 + 0.10s
Under the second plan, the representative earns a fixed monthly salary of $1200, regardless of his sales.
To find the point where the first plan becomes more lucrative, we need an inequality that compares the earnings from the first plan to the earnings from the second plan.
In this case, we want the earnings from the first plan to be greater than the earnings from the second plan. So the inequality will be:
Earnings from the first plan > Earnings from the second plan
Substituting the expressions for the earnings, we get:
$300 + 0.10s > $1200
Now, we can solve this inequality to find the amount of sales, represented by "s", for which the representative would make more money with the first plan.
$300 + 0.10s > $1200
0.10s > $1200 - $300
0.10s > $900
To isolate "s", we divide both sides of the inequality by 0.10:
s > $900 / 0.10
Simplifying, we get:
s > $9000
Therefore, for an amount of sales greater than $9000, the representative would make more money with the first plan.