When hired at a new job selling jewelry, you are given two pay options:
Option A: Base salary of $16,000 a year, with a commission of 10% of your sales
Option B: Base salary of $20,000 a year, with a commission of 3% of your sales
In order for option A to produce a larger income, you would need sell at least $_____ of jewelry?
16,000 + .1 s = 20,000 + .03 s
.07 s = 4,000
s = 400,000/7
To determine the sales amount needed for option A to produce a larger income, we can set up an equation. Let's represent the sales amount with 'x'.
For option A, the income would be the base salary plus the commission:
Income_A = $16,000 + 0.10x
For option B, the income would be the base salary plus the commission:
Income_B = $20,000 + 0.03x
To find the sales amount needed for option A to produce a larger income, we need to set up the following inequality:
Income_A > Income_B
$16,000 + 0.10x > $20,000 + 0.03x
Now, let's solve the inequality to find the minimum value of 'x' needed for option A to produce a larger income:
0.10x - 0.03x > $20,000 - $16,000
0.07x > $4,000
x > $4,000 / 0.07
x > $57,142.86
Therefore, in order for option A to produce a larger income, you would need to sell at least $57,142.86 worth of jewelry.
To determine the amount of jewelry you need to sell in order for option A to produce a larger income, we can set up an equation and solve for the sales amount.
Let's represent the sales amount by "x."
For Option A, the total income would be the base salary plus the commission. The commission is calculated as 10% of the sales, so it would be 0.10x. Hence, the income for Option A would be $16,000 + 0.10x.
For Option B, the total income would be the base salary plus the commission, which is 3% of the sales, or 0.03x. Hence, the income for Option B would be $20,000 + 0.03x.
We can write the equation to compare the two options:
$16,000 + 0.10x > $20,000 + 0.03x
Now, let's solve for x:
$16,000 - $20,000 > 0.03x - 0.10x
-$4,000 > -0.07x
To isolate x, we divide both sides of the inequality by -0.07, remembering that dividing by a negative number flips the inequality:
$4,000/-0.07 < x
Dividing $4,000 by -0.07 gives us:
-57,142.85 < x
Therefore, to make Option A produce a larger income, you would need to sell at least $57,142.85 worth of jewelry.