# Difference 3875

The four numbers are in a ratio of 5:7:4:6. Their difference is equal to -84. Specify these numbers.

a =  35
b =  49
c =  28
d =  42
k =  7

## Step-by-step explanation:

a=5k
b = 7k
c = 4k
d = 6k
a-b-c-d=-84

a=5·k
b = 7·k
c = 4·k
d = 6·k
a-b-c-d=-84

a-5k = 0
b-7k = 0
c-4k = 0
d-6k = 0
a-b-c-d = -84

Row 5 - Row 1 → Row 5
a-5k = 0
b-7k = 0
c-4k = 0
d-6k = 0
-b-c-d+5k = -84

Row 5 + Row 2 → Row 5
a-5k = 0
b-7k = 0
c-4k = 0
d-6k = 0
-c-d-2k = -84

Row 5 + Row 3 → Row 5
a-5k = 0
b-7k = 0
c-4k = 0
d-6k = 0
-d-6k = -84

Row 5 + Row 4 → Row 5
a-5k = 0
b-7k = 0
c-4k = 0
d-6k = 0
-12k = -84

k = -84/-12 = 7
d = 0+6k = 0+6 · 7 = 42
c = 0+4k = 0+4 · 7 = 28
b = 0+7k = 0+7 · 7 = 49
a = 0+5k = 0+5 · 7 = 35

a = 35
b = 49
c = 28
d = 42
k = 7

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