Crowns

1180 crowns are divided into three: A got 20% less than B, and C got 15% more than B. How many got A, B, and C?

Correct answer:

A =  320
B =  400
C =  460

Step-by-step explanation:


A+B+C = 1180
A = (1-20/100)·B
C = (1+15/100)·B

A+B+C = 1180
100A-80B = 0
115B-100C = 0

Pivot: Row 1 ↔ Row 2
100A-80B = 0
A+B+C = 1180
115B-100C = 0

Row 2 - 1/100 · Row 1 → Row 2
100A-80B = 0
1.8B+C = 1180
115B-100C = 0

Pivot: Row 2 ↔ Row 3
100A-80B = 0
115B-100C = 0
1.8B+C = 1180

Row 3 - 1.8/115 · Row 2 → Row 3
100A-80B = 0
115B-100C = 0
2.565C = 1180


C = 1180/2.56521739 = 460
B = 0+100C/115 = 0+100 · 460/115 = 400
A = 0+80B/100 = 0+80 · 400/100 = 320

A = 320
B = 400
C = 460

Our linear equations calculator calculates it.



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