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Erica receives an annual salary of $38,000 plus a commission of 20 per

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Erica receives an annual salary of $38,000 plus a commission of 20 per  [#permalink]

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New post 08 Jan 2018, 23:55
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Erica receives an annual salary of $38,000 plus a commission of 20 percent on sales she makes in excess of $90,000 while Carla receives an annual salary of $24,000 plus a 10 percent commission on her total annual sales only if they exceed $150,000. If Erica earned twice as much as Carla, and both realized equal sales for their company, what must the total annual sales made by each?

A. $95,000
B. $120,000
C. $140,000
D. $160,000
E. $180,000

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Erica receives an annual salary of $38,000 plus a commission of 20 per  [#permalink]

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New post 09 Jan 2018, 14:48
Bunuel wrote:
Erica receives an annual salary of $38,000 plus a commission of 20 percent on sales she makes in excess of $90,000 while Carla receives an annual salary of $24,000 plus a 10 percent commission on her total annual sales only if they exceed $150,000. If Erica earned twice as much as Carla, and both realized equal sales for their company, what must the total annual sales made by each?

A. $95,000
B. $120,000
C. $140,000
D. $160,000
E. $180,000

Use answer choices
Algebra is not much help here. The variables cancel (see below). Start with Answer C to get a benchmark.

C) $140,000. If both sold $140,000
Erica - Erica gets a 20% commission only on sales over $90,000

Amount of sales greater than $90,000:
(140,000 - 90,000) = $50,000

Erica's 20% commission on $50,000: .2*50,000= $10,000

Erica's total earnings: Base + Commission
$38,000 + $10,000 = $48,000

Carla
Gets no commission. (She gets commission only on sales greater than $150,000.)

Carla's total earnings: Base = $24,000

Erica earned twice as much as Carla?
$48,000 = 2($24,000) Correct

Answer

Algebra
IMO, unless you really prefer algebra, avoid. The moment I figured out that variables canceled each other, I moved to answer choices.

Erica's earnings:
$38,000 + .20(x - $90,000)
$38,000 + .20x - $18,000
$20,000 + .20x

Carla's earnings:
$24,000 + .10(x - $150,000)
$24,000 + .10x - $15,000
$9,000 + .10x

Erica earns twice as much as Carla:
$20,000 + .20x = 2($9,000 + .10x)
$20,000 + .20x = $18,000 + .20x
$20,000 = $18,000
False. No solution. The variables canceled each other.

There is only one possibility: commissions for Carla cannot figure in. (Commissions for Erica figure in. Answer choices are all > $90,000.)

So Erica, earning (Base + Commission), earns twice as much as Carla, who earns Base only.
38,000 + .20(x-90,000) = (2)* 24,000
38,000 + .20x - 18,000 = 48,000
20,000 + .2x = 48,000
.2x = 28,000
x = 28,000/.20
x = $140,000

Answer
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Erica receives an annual salary of $38,000 plus a commission of 20 per &nbs [#permalink] 09 Jan 2018, 14:48
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