Banknotes 34711

55 banknotes worth 133000 CZK, how many 1000 CZK banknotes, how many 2000 CZK banknotes, how many 5000 CZK banknotes if we know that the number of 2000 CZK banknotes is four fewer than the number of 1000 CZK banknotes

Correct answer:

a =  22
b =  18
c =  15

Step-by-step explanation:


55=a+b+c
1000a+2000b+5000c = 133000
b = a-4

55=a+b+c
1000·a+2000·b+5000·c = 133000
b = a-4

a+b+c = 55
1000a+2000b+5000c = 133000
a-b = 4

Pivot: Row 1 ↔ Row 2
1000a+2000b+5000c = 133000
a+b+c = 55
a-b = 4

Row 2 - 1/1000 · Row 1 → Row 2
1000a+2000b+5000c = 133000
-b-4c = -78
a-b = 4

Row 3 - 1/1000 · Row 1 → Row 3
1000a+2000b+5000c = 133000
-b-4c = -78
-3b-5c = -129

Pivot: Row 2 ↔ Row 3
1000a+2000b+5000c = 133000
-3b-5c = -129
-b-4c = -78

Row 3 - -1/-3 · Row 2 → Row 3
1000a+2000b+5000c = 133000
-3b-5c = -129
-2.333c = -35


c = -35/-2.33333333 = 15
b = -129+5c/-3 = -129+5 · 15/-3 = 18
a = 133000-2000b-5000c/1000 = 133000-2000 · 18-5000 · 15/1000 = 22

a = 22
b = 18
c = 15

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