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# Over the last three years, Salesperson A has earned twice as much as Salesperson B, who in turn has averaged 50% more than Salesperson C. Th

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Over the last three years, Salesperson A has earned twice as much as Salesperson B, who in turn has averaged 50% more than Salesperson C. The three combined to make \$220,000 over the three years. How much did Salesperson B earn on average in any year?

Guest Aug 3, 2014

#3
+4471
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Sally = y

Sue = z

y = 200

Before z = 3z, y = 2z

If y = 200, then 2z = 200 --> z = 100 before, now z = 3z = 3(100) = \$300.

AzizHusain  Aug 3, 2014
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#1
+4471
+5

Convert from verbal to mathematical:

A = 2B (twice as much)

B = 0.5C + C (50% more than C - must add the + C since B earned 50% more than C plus the actual amount C made)

A + B + C = \$220,000

By substituting 2B for A, we obtain 2B + B + C = 220,000, then 3B + C = 220,000 --> C = 220,000 - 3B

Then, we substitute for C in B = 0.5C + C --> B = 0.5(220,000 - 3B) + 220,000 - 3B

B = 110,000 - 1.5B + 220,000 - 3B

B = 330,000 - 4.5B

5.5B = 330,000

B = \$60,000.

Since the 3 made \$220,000 over 3 years...then, on average, B made 60,000 / 3 = \$20,000 in any year.

To check:

A = 2B = 2(60,000) = \$120,000

C = 220,000 - 3B = 220,000 - 3(60,000) = 220,000 - 180,000 = \$40,000

A + B + C = 220,000?

\$120,000 + \$60,000 + \$40,000 = \$220,000...Yes.

AzizHusain  Aug 3, 2014
#2
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Sally makes \$200 per week. Before Sue had her pay tripled, Sally made twice as much as Sue. How much does Sue now make per week?

Guest Aug 3, 2014
#3
+4471
+5

Sally = y

Sue = z

y = 200

Before z = 3z, y = 2z

If y = 200, then 2z = 200 --> z = 100 before, now z = 3z = 3(100) = \$300.

AzizHusain  Aug 3, 2014

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