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Over the last 3 years salesperson A has earned twice as much as salesperson B, who in turned averaged 50% more then 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 17, 2018

#1**+2 **

Let salesperson C's earnings =C

Salesperson B's earnings =1.5C

Salesperson A's earnings =3C

C + 1.5C + 3C = $220,000

5.5C = $220,000

C = $220,000 / 5.5

C = $40,000 - total earnings of salesperson C over 3 years.

$40,000 x 1.5 = $60,000 - total earnings of salespeson B over 3 years.

**$60,000 / 3 = $20,000 - Salesperson B's average earnings per year for 3 years.**

Guest Aug 17, 2018

#2**+2 **

Over the last 3 years salesperson A has earned twice as much as salesperson B, who in turned averaged 50% more then salesperson C. The three combined to make $220 000 over the three years. How much did salesperson B earn on average in any year?

\(a=2b\\ \color{blue}b=\frac{a}{2}\\ b=1.5c\\ c=\frac{b}{1.5}=\frac{\frac{a}{2}}{1.5}\\ \color{blue}c=\frac{a}{3}\)

\((a+b+c)\cdot 3\ years=220000\$\\ (a+\frac{a}{2}+\frac{a}{3})\cdot 3\ years=220000\$\\ \frac{6a+3a+2a}{2\cdot3}=\frac{220000\$}{3\ years}\\ 11a=\frac{6\cdot 220000\$}{3\ years}\\ a=\frac{6\cdot 220000\$}{11\cdot 3\cdot years}\)

\(a=40000\ \$/year\)

\(b=\frac{a}{2}=\frac{40000}{2}\cdot \frac{\$}{year}\)

\(b=20000\ \$\ /\ year\)

Salesperson B earns 20 000 $ / year.

!

asinus Aug 17, 2018