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​

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.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b