A salesperson has two job offers. Company A offers a weekly salary of $150 plus commission of 6% of sales. Company B offers a weekly salary of $300 plus commission of 3% of sales. What is the amount of sales above which Company A's offer is the better of the two?
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To determine the amount of sales above which Company A's offer is better than Company B's, we need to find the point where the earnings from Company A exceed the earnings from Company B.
Let's first calculate the earnings for each company based on the given information:
For Company A:
Weekly salary: $150
Commission rate: 6% of sales
For Company B:
Weekly salary: $300
Commission rate: 3% of sales
Let's assume the amount of sales is 'x'.
For Company A, the total earnings can be calculated using the formula:
Earnings from Company A = Weekly salary + Commission on sales
Earnings from Company A = $150 + (6% of x)
For Company B, the total earnings can be calculated using the formula:
Earnings from Company B = Weekly salary + Commission on sales
Earnings from Company B = $300 + (3% of x)
Now, we have the two equations to compare the earnings of both companies:
Earnings from Company A = $150 + (6% of x)
Earnings from Company B = $300 + (3% of x)
To find the amount of sales above which Company A's offer is better, we need to solve the inequality:
Earnings from Company A > Earnings from Company B
Let's substitute the formulas with the respective variables:
$150 + (6% of x) > $300 + (3% of x)
Now, let's solve the inequality:
$150 + (0.06x) > $300 + (0.03x)
Subtracting $150 from both sides:
(0.06x) - (0.03x) > $300 - $150
Simplifying:
0.03x > $150
Dividing both sides by 0.03:
x > $150 / 0.03
x > $5,000
Therefore, the amount of sales must be above $5,000 for Company A's offer to be better than Company B's offer.