# Summands 54861 ​​

Can you divide the number 64.9 into three summands so that the first with the second is in the ratio 4:5 and the third with the first in the ratio 7:3?

a =  14.16
b =  17.7
c =  33.04

### Step-by-step explanation:

a+b+c=64.9
a=4/5·b
c=7/3·a

a+b+c = 64.9
5a-4b = 0
7a-3c = 0

Pivot: Row 1 ↔ Row 3
7a-3c = 0
5a-4b = 0
a+b+c = 64.9

Row 2 - 5/7 · Row 1 → Row 2
7a-3c = 0
-4b+2.143c = 0
a+b+c = 64.9

Row 3 - 1/7 · Row 1 → Row 3
7a-3c = 0
-4b+2.143c = 0
b+1.429c = 64.9

Row 3 - 1/-4 · Row 2 → Row 3
7a-3c = 0
-4b+2.143c = 0
1.964c = 64.9

c = 64.9/1.96428571 = 33.04
b = 0-2.1428571428571c/-4 = 0-2.14285714 · 33.04/-4 = 17.7
a = 0+3c/7 = 0+3 · 33.04/7 = 14.16

a = 354/25 = 14.16
b = 177/10 = 17.7
c = 826/25 = 33.04

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