Number sum calculation

Of the four numbers, the second is five larger than the first, the third two smaller than the first, and the fourth is twice larger than the first. Find these numbers if their sum is 38.

Final Answer:

a = 7
b = 12
c = 5
d = 14

Step-by-step explanation:

b=5+a
c =a-2
d=2a
a+b+c+d=38

b=5+a
c =a-2
d=2·a
a+b+c+d=38

a-b = -5
a-c = 2
2a-d = 0
a+b+c+d = 38

Pivot: Row 1 ↔ Row 3
2a-d = 0
a-c = 2
a-b = -5
a+b+c+d = 38

Row 2 - 1/2 · Row 1 → Row 2
2a-d = 0
-c+0.5d = 2
a-b = -5
a+b+c+d = 38

Row 3 - 1/2 · Row 1 → Row 3
2a-d = 0
-c+0.5d = 2
-b+0.5d = -5
a+b+c+d = 38

Row 4 - 1/2 · Row 1 → Row 4
2a-d = 0
-c+0.5d = 2
-b+0.5d = -5
b+c+1.5d = 38

Pivot: Row 2 ↔ Row 3
2a-d = 0
-b+0.5d = -5
-c+0.5d = 2
b+c+1.5d = 38

Row 4 + Row 2 → Row 4
2a-d = 0
-b+0.5d = -5
-c+0.5d = 2
c+2d = 33

Row 4 + Row 3 → Row 4
2a-d = 0
-b+0.5d = -5
-c+0.5d = 2
2.5d = 35

d = 35/2.5 = 14
c = 2-0.5d/-1 = 2-0.5 · 14/-1 = 5
b = -5-0.5d/-1 = -5-0.5 · 14/-1 = 12
a = 0+d/2 = 0+14/2 = 7

a = 7
b = 12
c = 5
d = 14

Our linear equations calculator calculates it.