Together 4530

Nela, Olga, and Pavla saved up for a joint gift.
Olga saved a quarter less than Nela. Pavla saved 140 crowns more than Nela.
All three girls together saved three times more than Nela alone. How much did anyone save?

Correct answer:

n =  560
o =  420
p =  700

Step-by-step explanation:


o = n - n/4
p = 140 +n
o+n+p = 3n

o = n - n/4
p = 140 +n
o+n+p = 3·n

3n-4o = 0
n-p = -140
2n-o-p = 0

Row 2 - 1/3 · Row 1 → Row 2
3n-4o = 0
1.333o-p = -140
2n-o-p = 0

Row 3 - 2/3 · Row 1 → Row 3
3n-4o = 0
1.333o-p = -140
1.667o-p = 0

Pivot: Row 2 ↔ Row 3
3n-4o = 0
1.667o-p = 0
1.333o-p = -140

Row 3 - 1.33333333/1.66666667 · Row 2 → Row 3
3n-4o = 0
1.667o-p = 0
-0.2p = -140


p = -140/-0.2 = 700
o = 0+p/1.66666667 = 0+700/1.66666667 = 420
n = 0+4o/3 = 0+4 · 420/3 = 560

n = 560
o = 420
p = 700

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