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: [tex]\dfrac{1}{6}p[/tex]
Another number be q.
Two thirds another number q: [tex]\dfrac{2}{3}q[/tex]
5 more than two thirds another number q: [tex]\dfrac{2}{3}q+5[/tex]
According to the question, one sixth of a number p is equal to 5 more than two thirds another number q.
[tex]\dfrac{1}{6}p=\dfrac{2}{3}q+5[/tex]
Subtract 5 from both sides.
[tex]\dfrac{1}{6}p-5=\dfrac{2}{3}q[/tex]
Multiply both sides by [tex]\dfrac{3}{2}[/tex].
[tex]\dfrac{3}{2}(\dfrac{1}{6}p-5)=\dfrac{3}{2}\times \dfrac{2}{3}q[/tex]
[tex]\dfrac{3}{2}(\dfrac{1}{6}p)+\dfrac{3}{2}(-5)=q[/tex]
[tex]\dfrac{1}{4}p-\dfrac{15}{2}=q[/tex]
Therefore, the required solution is [tex]q=\dfrac{1}{4}p-\dfrac{15}{2}[/tex].
