Question

One sixth of a number,p, is 5 more than two thirds another number, q. Solve for p

Answer 1

Given:

One sixth of a number, p, is 5 more than two thirds another number, q.

To find:

The value of q.

Solution:

Consider p be a number.

One sixth of a number p:
`(1)/(6)p`

Another number be q.

Two thirds another number q:
`(2)/(3)q`

5 more than two thirds another number q:
`(2)/(3)q+5`

According to the question, one sixth of a number p is equal to 5 more than two thirds another number q.

`(1)/(6)p=(2)/(3)q+5`

Subtract 5 from both sides.

`(1)/(6)p-5=(2)/(3)q`

Multiply both sides by
`(3)/(2)`.

`(3)/(2)((1)/(6)p-5)=(3)/(2)* (2)/(3)q`

`(3)/(2)((1)/(6)p)+(3)/(2)(-5)=q`

`(1)/(4)p-(15)/(2)=q`

Therefore, the required solution is
`q=(1)/(4)p-(15)/(2)`.