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?
+4473 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.
+4473 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.
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?
+4473 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.
