Question

5/8p−3/4=4

A) p=95/32

B) p=26/5

C) p=38/5

Answer 1

5/8p = 4 + 3/4
5/8 p= 19/4
P= 19/4 / 5/8
P= 19/4 x 8/5
P= 38/5
The answer is C

Answer 2

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5)/(8)p-(3)/(4)=4 } \end{gathered}$}}`

Add 3/4 to both sides.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5)/(8)p=4+(3)/(4) } \end{gathered}$}}`

Convert 4 to the fraction 16/4.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5)/(8)p=(16)/(4) +(3)/(4) } \end{gathered}$}}`

Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5)/(8)p=(16+3)/(4) \longmapsto \ \ Add } \end{gathered}$}}`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5)/(8)p=(19)/(4) } \end{gathered}$}}`

Multiply both sides by 8/5, the reciprocal of 5/8.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=(19)/(4)*\left((5)/(8)\right) } \end{gathered}$} }`

Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=(19*8)/(4*5 )\longmapsto \ Multiply } \end{gathered}$}}`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=(152)/(20) } \end{gathered}$}}`

We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=(152)/(20) \ \ \longmapsto \ p=(152/4)/(20/4)=(38)/(5) } \end{gathered}$}}`

Therefore, the answer is option C.