Answer:
Option C [tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
Step-by-step explanation:
we have that
The given equation is
[tex]-16p+37=49-21p[/tex]
Solve for p
Group terms that contain the same variable
[tex]-16p+21p=49-37[/tex]
Combine like terms
[tex]5p=12[/tex]
[tex]p=12/5[/tex]
[tex]p=2.4[/tex]
we know that
If a equation has the same solution as the given equation, then the solution of the given equation must satisfy the equation
Verify each case
case A) we have
[tex]2+1.25p=-3.75p+10[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]2+1.25(2.4)=-3.75(2.4)+10[/tex]
[tex]5=1[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case B) we have
[tex]-55+12p=5p+16[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-55+12(2.4)=5(2.4)+16[/tex]
[tex]-26.2=28[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case C) we have
[tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex](3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)[/tex]
[tex]4=4[/tex] ----> is true
therefore
The equation has the same solution as the given equation
case D) we have
[tex]-14+6p=-9-6p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-14+6(2.4)=-9-6(2.4)[/tex]
[tex]0.4=-5.4[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
