Number ratio

Determine three numbers in the ratio 1 : 2/3 : 3/4 whose sum equals the smallest three-digit number.

Final Answer:

a =  60
b =  40
c =  45

Step-by-step explanation:


2/3 a = b
3/4 b = 2/3 c
a+b=100

2/3·a = b
3/4·b = 2/3·c
a+b=100

2a-3b = 0
9b-8c = 0
a+b = 100

Row 3 - 1/2 · Row 1 → Row 3
2a-3b = 0
9b-8c = 0
2.5b = 100

Row 3 - 2.5/9 · Row 2 → Row 3
2a-3b = 0
9b-8c = 0
2.222c = 100


c = 100/2.22222222 = 45
b = 0+8c/9 = 0+8 · 45/9 = 40
a = 0+3b/2 = 0+3 · 40/2 = 60

a = 60
b = 40
c = 45

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