# Sum of three numbers

The sum of three numbers from which the second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine these numbers.

x =  40
y =  32
z =  24

## Step-by-step explanation:

x+y+z=96
y=x-0.20x
z=y-0.25y

x+y+z=96
y=x-0.20·x
z=y-0.25·y

x+y+z = 96
0.8x-y = 0
0.75y-z = 0

Row 2 - 0.8 · Row 1 → Row 2
x+y+z = 96
-1.8y-0.8z = -76.8
0.75y-z = 0

Row 3 - 0.75/-1.8 · Row 2 → Row 3
x+y+z = 96
-1.8y-0.8z = -76.8
-1.333z = -32

z = -32/-1.33333333 = 24
y = -76.8+0.8z/-1.8 = -76.8+0.8 · 24/-1.8 = 32
x = 96-y-z = 96-32-24 = 40

x = 40
y = 32
z = 24

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