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BlackZzzverrR [31]
3 years ago
7

a number 84 is divided into two parts. if the difference between half of the first part and one-third of the second part is 12,

find two parts of number.
Mathematics
1 answer:
ra1l [238]3 years ago
6 0

The first part is 48 and the second part is 36.

Step-by-step explanation:

Let,

The first half = x

The second half = y

According to given statement;

x+y=84       Eqn 1

\frac{1}{2}x-\frac{1}{3}y=12\ \ \ Eqn\ 2

Multiplying Eqn 1 by \frac{1}{2}

\frac{1}{2}(x+y=84)\\\\\frac{1}{2}x+\frac{1}{2}y=42\ \ \ Eqn\ 3

Subtracting Eqn 2 from Eqn 3

(\frac{1}{2}x+\frac{1}{2}y)-(\frac{1}{2}x-\frac{1}{3}y=42-12\\\\\frac{1}{2}x+\frac{1}{2}y-\frac{1}{2}x+\frac{1}{3}y=30\\\\\frac{1}{2}y+\frac{1}{3}y=30\\\\\frac{3y+2y}{6}=30\\\\\frac{5y}{6}=30

Multiplying both sides by \frac{6}{5}

\frac{6}{5}*\frac{5}{6}y=30*\frac{6}{5}\\\\y=\frac{180}{5}\\\\y=36

Putting y=36 in Eqn 1

x+36=84\\x=84-36\\x=48

The first part is 48 and the second part is 36.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/10046556
  • brainly.com/question/100704

#LearnwithBrainly

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From the picture attached,

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