Answer:
The value of p = 6.
Step-by-step explanation:
Given the expression
[tex]\left(3.14\cdot \:18\right)\cdot \:17.5=3.14\left(3p\cdot \:17.5\right)[/tex]
Solving for p
[tex]\left(3.14\cdot \:18\right)\cdot \:17.5=3.14\left(3p\cdot \:17.5\right)[/tex]
switch sides
[tex]3.14\left(3p\cdot \:17.5\right)=\left(3.14\cdot \:18\right)\cdot \:17.5[/tex]
Remove parentheses: (a) = a
[tex]3.14\left(3p\cdot \:17.5\right)=3.14\cdot \:18\cdot \:17.5[/tex]
Multiply the numbers: [tex]3.14\cdot \:18\cdot \:17.5=989.1[/tex]
[tex]3.14\left(3p\cdot \:17.5\right)=989.1[/tex]
Multiply both sides by 100
[tex]3.14\cdot \:3p\cdot \:17.5\cdot \:100=989.1\cdot \:100[/tex]
Refine
[tex]16485p=98910[/tex]
Divide both sides by 16485
[tex]\frac{16485p}{16485}=\frac{98910}{16485}[/tex]
Simplify
[tex]p=6[/tex]
Therefore, the value of p = 6.
