Sure! Let's solve the equation step-by-step to find the value of \( p \). Given the equation:
[tex]\[
\frac{p-3.1}{6.7} = \frac{4.5}{5}
\][/tex]
First, we'll solve the right side of the equation:
[tex]\[
\frac{4.5}{5} = 0.9
\][/tex]
The equation now becomes:
[tex]\[
\frac{p-3.1}{6.7} = 0.9
\][/tex]
Next, we need to solve for \( p \). We can do this by isolating \( p \). First, multiply both sides of the equation by \( 6.7 \) to clear the denominator on the left side:
[tex]\[
p - 3.1 = 0.9 \cdot 6.7
\][/tex]
Calculate \( 0.9 \cdot 6.7 \):
[tex]\[
0.9 \cdot 6.7 = 6.03
\][/tex]
Now the equation is:
[tex]\[
p - 3.1 = 6.03
\][/tex]
To isolate \( p \), add \( 3.1 \) to both sides of the equation:
[tex]\[
p = 6.03 + 3.1
\][/tex]
Perform the addition:
[tex]\[
p = 9.13
\][/tex]
So, the solution is:
[tex]\[
p = 9.13
\][/tex]
Let's check the given possible values of \( p \):
1. \( p = -9.47 \)
2. \( p = 2.93 \)
3. \( p = 9.13 \)
4. \( p = 21.53 \)
The value that matches our solution is [tex]\( p = 9.13 \)[/tex]. Thus, the correct value of [tex]\( p \)[/tex] is [tex]\( 9.13 \)[/tex].
