Question

A rational number is such that when you multiply it by 5
2
and add 2
3
to the
product, you get 7
12

. What is the number?

Answer 1

Let the number be x

Multiply by 5/2=x*5/2=5x/2

No. to be added=2/3=5x/2+2/3

Now according to question

5x/2+2/3=7/12

5x/2=7/12-2/3

5x/2=(7-8)/12 ( lcm of a3 and 12 is 12)

5x/2=-1/12

5x=-1/12*2

5x=-1/6

x=-1/6/5

x=-5/6 is the answer.

You can also verify the answer by putting the value of x in the eauation.

Hope this helps you...

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Answer 2

Let the rational be x.

According to the question,

x × (5/2) + 2/3 = -7/12

⇒ 5x/2 + 2/3 = -7/12

⇒ 5x/2 = -7/12 – 2/3

⇒ 5x/2 = (-7- 8)/12

⇒ 5x/2 = -15/12

⇒ 5x/2 = -5/4

⇒ x = (-5/4) × (2/5)

⇒ x = – 10/20

⇒ x = -½

Therefore, the rational number is -½.