Collecting 7523

The four friends received money for collecting paper as follows: Mirko received a quarter of the entire amount, Robo received a third of the remaining money, and Boris received half of the second remaining money. Peter had 1.50 euros left. How many crowns did Mirko and Robo get together?

Correct answer:

s = 3 Eur

Step-by-step explanation:

m = x/4
r = (x-m)/3
b = (x-m-r)/2
x = m+r+b+1.5
s = m+r

4m-x = 0
m+3r-x = 0
2b+m+r-x = 0
b+m+r-x = -1.5
m+r-s = 0

Pivot: Row 1 ↔ Row 3
2b+m+r-x = 0
m+3r-x = 0
4m-x = 0
b+m+r-x = -1.5
m+r-s = 0

Row 4 - 1/2 · Row 1 → Row 4
2b+m+r-x = 0
m+3r-x = 0
4m-x = 0
0.5m+0.5r-0.5x = -1.5
m+r-s = 0

Pivot: Row 2 ↔ Row 3
2b+m+r-x = 0
4m-x = 0
m+3r-x = 0
0.5m+0.5r-0.5x = -1.5
m+r-s = 0

Row 3 - 1/4 · Row 2 → Row 3
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
0.5m+0.5r-0.5x = -1.5
m+r-s = 0

Row 4 - 0.5/4 · Row 2 → Row 4
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
0.5r-0.375x = -1.5
m+r-s = 0

Row 5 - 1/4 · Row 2 → Row 5
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
0.5r-0.375x = -1.5
r-s+0.25x = 0

Row 4 - 0.5/3 · Row 3 → Row 4
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
-0.25x = -1.5
r-s+0.25x = 0

Row 5 - 1/3 · Row 3 → Row 5
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
-0.25x = -1.5
-s+0.5x = 0

Pivot: Row 4 ↔ Row 5
2b+m+r-x = 0
4m-x = 0
3r-0.75x = 0
-s+0.5x = 0
-0.25x = -1.5

x = -1.5/-0.25 = 6
s = 0-0.5x/-1 = 0-0.5 · 6/-1 = 3
r = 0+0.75x/3 = 0+0.75 · 6/3 = 1.5
m = 0+x/4 = 0+6/4 = 1.5
b = 0-m-r+x/2 = 0-1.5-1.5+6/2 = 1.5

b = 3/2 = 1.5
m = 3/2 = 1.5
r = 3/2 = 1.5
s = 3
x = 6

Our linear equations calculator calculates it.