# Bonuses

Five company employees were paid bonuses, so each successor received 550 USD less than the previous employee. How much did everyone get if a total of USD 11,000 has paid?

a =  3300
b =  2750
c =  2200
d =  1650
f =  1100

## Step-by-step explanation:

a+b+c+d+f = 11000
b = a-550
c = b-550
d = c-550
f = d-550

a+b+c+d+f = 11000
a-b = 550
b-c = 550
c-d = 550
d-f = 550

Row 2 - Row 1 → Row 2
a+b+c+d+f = 11000
-2b-c-d-f = -10450
b-c = 550
c-d = 550
d-f = 550

Row 3 - 1/-2 · Row 2 → Row 3
a+b+c+d+f = 11000
-2b-c-d-f = -10450
-1.5c-0.5d-0.5f = -4675
c-d = 550
d-f = 550

Row 4 - 1/-1.5 · Row 3 → Row 4
a+b+c+d+f = 11000
-2b-c-d-f = -10450
-1.5c-0.5d-0.5f = -4675
-1.33333d-0.33333f = -2566.66667
d-f = 550

Row 5 - 1/-1.33333333 · Row 4 → Row 5
a+b+c+d+f = 11000
-2b-c-d-f = -10450
-1.5c-0.5d-0.5f = -4675
-1.33333d-0.33333f = -2566.66667
-1.25f = -1375

f = -1375/-1.25 = 1100
d = -2566.66666667+0.33333333333333f/-1.33333333 = -2566.66666667+0.33333333 · 1100/-1.33333333 = 1650
c = -4675+0.5d+0.5f/-1.5 = -4675+0.5 · 1650+0.5 · 1100/-1.5 = 2200
b = -10450+c+d+f/-2 = -10450+2200+1650+1100/-2 = 2750
a = 11000-b-c-d-f = 11000-2750-2200-1650-1100 = 3300

a = 3300
b = 2750
c = 2200
d = 1650
f = 1100

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