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Sum of digits in a three digit number is nine. The tens digit is half sum of the other two and the hundreds digit is half the units digits. Find the number​

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Answer:

234

Step-by-step explanation:

Let the digit in the hundreds place be a, the digit in the tens place be b and the digit in the ones place be c. So a b c is the number.

(Based on the question) a + b + c = 9 ----- Equation 1

From Equation 1, you can get:

2a + 2b + 2c = 18 ----- Equation 2

(Based on the question) 2b = a + c ------ Equation 3

(Based on the question) 2a = c ----- Equation 4

Replace the c in Equation 3 with Equation 4:

2b = a + 2a

Evaluate.

2b = 3a ----- Equation 5

Replace all the values of b and c with Equations 4 and 5 respectively into Equation 1 (Check underlined Equations to realise that all terms equal to a term in a):

2a + 3a + 2(2a) = 18

Evaluate.

2a + 3a + 4a = 18

9a = 18

Find a.

a = 18 ÷ 9

a = 2

Based on Equation 4, find c.

c = 2 × 2

c = 4

Based on Equation 1, find b.

b = 9 - 2 - 4

b = 3

Piecing together the values of a, b and c, the number is 234.

X + Y + Z = 9
Y = (X+Z)/2
X = Z/2
replacing X in Y
Y = (Z/2 + Z)/2 = 3Z/4
Putting equations X and Y in equation ( X + Y + Z = 9 )
We have,
Z/2 + 3Z/4 + Z = 9

Multiply through by 4
2Z + 3Z + 4Z = 36
Z = 4
Replacing Z to solve for X and Y
Y = 3
X = 2

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