Question

Complete Part A and Part B using the equation

7.4p +2.6 = 8.3p + 5.3
Part A
Write an equivalent equation by eliminating the decimals.
Part B
Solve the equation. p=

Answer 1

Rewritten:
`(37)/(5)p+(13)/(5) =(83)/(10) p+(53)/(10)`

Solved:
`p=-3`

Explanation:

A way you could rewrite the equation without decimals is with fractions.

• 7.4 is equal to
  `7(4)/(10)` or
  `(74)/(10)` which simplifies to
  `(37)/(5)`

• 2.6 is equal to
  `2(6)/(10)` or
  `(26)/(10)` which simplifies to
  `(13)/(5)`

• 8.3 is equal to
  `8(3)/(10)` or
  `(83)/(10)`

• and 5.3 is equal to
  `5(3)/(10)` or
  `(53)/(10)`

So the rewritten equation would look like
`(37)/(5)p+(13)/(5) =(83)/(10) p+(53)/(10)` .

In order to solve it, we want to get all of the variables, in this case "p," on one side of the equation.

• It will also help to have all the denominators be the same number. Since
  `(83)/(10)` and
  `(53)/(10)` cannot be simplified any further, we multiply
  `(37)/(5)` and
  `(13)/(5)` by
  `(2)/(2)` so they also have a denominator of 10.

To solve, we add
`(26)/(10)` to the right side and subtract
`(83)/(10) p` from the right side:

• The equation now looks like this:
  `(74)/(10)p-(83)/(10) p=(53)/(10)-(26)/(10)`

Now we can factor out the "p" from the left side:

• 
  `p((74)/(10)-(83)/(10))=(53)/(10)-(26)/(10)`

We can simplify
`(74)/(10)-(83)/(10)` and
`(53)/(10)-(26)/(10)` to
`(74-83)/(10)=-(9)/(10)` and
`(53-26)/(10)=(27)/(10)`:

• 
  `p(-(9)/(10))=(27)/(10)`

Then we would divide the right side by
`-(9)/(10)`:

• 
  `p=((27)/(10))/(-(9)/(10))`

Next we multiply the numerator by the reciprocal of the denominator:

• 
  `p=(27)/(10)(-(10)/(9) )`

Then we multiply:

• 
  `p=-(270)/(90)`

And finally, simplify:

• 
  `p=-3`