Collecting 3306

Four friends received money for collecting paper as follows: Mirko received a quarter of the total amount, Robo received a third of the rest of the money, and Boris received half of the money left by Mirko and Robo. Peter has 16 euros left. How many euros did Mirko and Robo get together?

Correct answer:

x = 32 Eur

Step-by-step explanation:

M=c/4
R = (c-M)/3
B = (c-M-R)/2
P = 16
c = M+R+B+P
x = M+R

4M-c = 0
M+3R-c = 0
2B+M+R-c = 0
P = 16
B+M+P+R-c = 0
M+R-x = 0

Pivot: Row 1 ↔ Row 3
2B+M+R-c = 0
M+3R-c = 0
4M-c = 0
P = 16
B+M+P+R-c = 0
M+R-x = 0

Row 5 - 1/2 · Row 1 → Row 5
2B+M+R-c = 0
M+3R-c = 0
4M-c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Pivot: Row 2 ↔ Row 3
2B+M+R-c = 0
4M-c = 0
M+3R-c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Row 3 - 1/4 · Row 2 → Row 3
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Row 5 - 0.5/4 · Row 2 → Row 5
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
P+0.5R-0.375c = 0
M+R-x = 0

Row 6 - 1/4 · Row 2 → Row 6
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
P+0.5R-0.375c = 0
R+0.25c-x = 0

Pivot: Row 3 ↔ Row 4
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
P+0.5R-0.375c = 0
R+0.25c-x = 0

Row 5 - Row 3 → Row 5
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5R-0.375c = -16
R+0.25c-x = 0

Row 5 - 0.5/3 · Row 4 → Row 5
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
-0.25c = -16
R+0.25c-x = 0

Row 6 - 1/3 · Row 4 → Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
-0.25c = -16
0.5c-x = 0

Pivot: Row 5 ↔ Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5c-x = 0
-0.25c = -16

Row 6 - -0.25/0.5 · Row 5 → Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5c-x = 0
-0.5x = -16

x = -16/-0.5 = 32
c = 0+x/0.5 = 0+32/0.5 = 64
R = 0+0.75c/3 = 0+0.75 · 64/3 = 16
P = 16/1 = 16
M = 0+c/4 = 0+64/4 = 16
B = 0-M-R+c/2 = 0-16-16+64/2 = 16

B = 16
M = 16
P = 16
R = 16
c = 64
x = 32

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