Subsequent 3312

We have to distribute 1200 euros to the five successful Olympic solvers so that the second and each subsequent one gets 50 euros less than the previous one. How many euros did each get?

Correct answer:

a =  340
b =  290
c =  240
d =  190
f =  140

Step-by-step explanation:


1200 = a + (a-50) + (a-100) + (a-150) + (a-200)
b = a-50
c = b-50
d = c-50
f = d- 50

5a = 1700
a-b = 50
b-c = 50
c-d = 50
d-f = 50

Row 2 - 1/5 · Row 1 → Row 2
5a = 1700
-b = -290
b-c = 50
c-d = 50
d-f = 50

Row 3 + Row 2 → Row 3
5a = 1700
-b = -290
-c = -240
c-d = 50
d-f = 50

Row 4 + Row 3 → Row 4
5a = 1700
-b = -290
-c = -240
-d = -190
d-f = 50

Row 5 + Row 4 → Row 5
5a = 1700
-b = -290
-c = -240
-d = -190
-f = -140


f = -140/-1 = 140
d = -190/-1 = 190
c = -240/-1 = 240
b = -290/-1 = 290
a = 1700/5 = 340

a = 340
b = 290
c = 240
d = 190
f = 140

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