a salesperson who must decide between two monthly income options:
Option A: Salary of $1642 per month, plus 8% of monthly sales
or Option B: Salary of $1900 per month, plus 6.5% of monthly sales
For what amount of monthly sales is Option A the better choice for Mike than Option B?
Let x = monthly sales. Write an appropriate inequality involving x and solve it algebraically. Write a sentence to carefully state the answer to the question. The sentence should have the form “Option A is the better choice if the monthly sales are more than _____.”
Easiest way to solve it is to begin by writing an equation where they are equal. So...
1642 + .08x = 1900 + .065x
Now, here's the thing. We're not looking to see what is equal. We are lookung to see when the first option is GREATER than the 2nd option. So we can say greater than (>) rather than equals (=).
1648 + .08x > 1900 + .065x
Do you understand:
1) How I got that?
2) How to solve it from there?
Not sure why that posted twice. Oh well. :-)
Thanks, I was on the right track
To determine for what amount of monthly sales Option A is better than Option B, we need to compare the incomes for both options.
For Option A, the income can be calculated by adding the fixed monthly salary of $1642 to the commission earned based on 8% of the monthly sales: Income_A = $1642 + 0.08x.
For Option B, the income can be calculated by adding the fixed monthly salary of $1900 to the commission earned based on 6.5% of the monthly sales: Income_B = $1900 + 0.065x.
We want to find the point at which Option A is better than Option B, so we need to determine when Income_A is greater than Income_B.
Setting up the inequality, we have:
Income_A > Income_B
$1642 + 0.08x > $1900 + 0.065x
Now, we can solve this inequality algebraically:
0.08x - 0.065x > $1900 - $1642
0.015x > $258
Dividing both sides by 0.015:
x > $258 / 0.015
x > $17,200
Therefore, Option A is the better choice if the monthly sales are more than $17,200.