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

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a system of equations and are looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

Related math problems and questions: