Question

Consider the following equation

Select the equation that has the same solution as the given equation.

Answer 1

Option C
`(3/2)p-5+(9/4)p=7-(5/4)p`

Explanation:

we have that

The given equation is

`-16p+37=49-21p`

Solve for p

Group terms that contain the same variable

`-16p+21p=49-37`

Combine like terms

`5p=12`

`p=12/5`

`p=2.4`

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

`2+1.25p=-3.75p+10`

substitute the value of p=2.4 in the equation and then compare the results

`2+1.25(2.4)=-3.75(2.4)+10`

`5=1` ----> is not true

therefore

The equation does not have the same solution as the given equation

case B) we have

`-55+12p=5p+16`

substitute the value of p=2.4 in the equation and then compare the results

`-55+12(2.4)=5(2.4)+16`

`-26.2=28` ----> is not true

therefore

The equation does not have the same solution as the given equation

case C) we have

`(3/2)p-5+(9/4)p=7-(5/4)p`

substitute the value of p=2.4 in the equation and then compare the results

`(3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)`

`4=4` ----> is true

therefore

The equation has the same solution as the given equation

case D) we have

`-14+6p=-9-6p`

substitute the value of p=2.4 in the equation and then compare the results

`-14+6(2.4)=-9-6(2.4)`

`0.4=-5.4` ----> is not true

therefore

The equation does not have the same solution as the given equation